Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 2*sin(x)=1
-
Equation x/2+x=12
-
Equation 3x^2-12=0
-
Equation x-11=-7
- Express {x} in terms of y where:
- 18*x+19*y=7
- -4*x+4*y=-9
- -20*x+14*y=16
- -4*x+14*y=-2
-
Identical expressions
- forty * one / five *(x- two *y)^ two + thirty-six * one / five *(x- two *y)*(two *x+y)+ twenty-five * one / five *(two *x+y)^ two - eight * one /sqrt(five)*(x- two *y)- fourteen * one /sqrt(five)*(two *x-y)+ one = zero
- 40 multiply by 1 divide by 5 multiply by (x minus 2 multiply by y) squared plus 36 multiply by 1 divide by 5 multiply by (x minus 2 multiply by y) multiply by (2 multiply by x plus y) plus 25 multiply by 1 divide by 5 multiply by (2 multiply by x plus y) squared minus 8 multiply by 1 divide by square root of (5) multiply by (x minus 2 multiply by y) minus 14 multiply by 1 divide by square root of (5) multiply by (2 multiply by x minus y) plus 1 equally 0
- forty multiply by one divide by five multiply by (x minus two multiply by y) to the power of two plus thirty minus six multiply by one divide by five multiply by (x minus two multiply by y) multiply by (two multiply by x plus y) plus twenty minus five multiply by one divide by five multiply by (two multiply by x plus y) to the power of two minus eight multiply by one divide by square root of (five) multiply by (x minus two multiply by y) minus fourteen multiply by one divide by square root of (five) multiply by (two multiply by x minus y) plus one equally zero
- 40*1/5*(x-2*y)^2+36*1/5*(x-2*y)*(2*x+y)+25*1/5*(2*x+y)^2-8*1/√(5)*(x-2*y)-14*1/√(5)*(2*x-y)+1=0
- 40*1/5*(x-2*y)2+36*1/5*(x-2*y)*(2*x+y)+25*1/5*(2*x+y)2-8*1/sqrt(5)*(x-2*y)-14*1/sqrt(5)*(2*x-y)+1=0
- 40*1/5*x-2*y2+36*1/5*x-2*y*2*x+y+25*1/5*2*x+y2-8*1/sqrt5*x-2*y-14*1/sqrt5*2*x-y+1=0
- 40*1/5*(x-2*y)²+36*1/5*(x-2*y)*(2*x+y)+25*1/5*(2*x+y)²-8*1/sqrt(5)*(x-2*y)-14*1/sqrt(5)*(2*x-y)+1=0
- 40*1/5*(x-2*y) to the power of 2+36*1/5*(x-2*y)*(2*x+y)+25*1/5*(2*x+y) to the power of 2-8*1/sqrt(5)*(x-2*y)-14*1/sqrt(5)*(2*x-y)+1=0
- 401/5(x-2y)^2+361/5(x-2y)(2x+y)+251/5(2x+y)^2-81/sqrt(5)(x-2y)-141/sqrt(5)(2x-y)+1=0
- 401/5(x-2y)2+361/5(x-2y)(2x+y)+251/5(2x+y)2-81/sqrt(5)(x-2y)-141/sqrt(5)(2x-y)+1=0
- 401/5x-2y2+361/5x-2y2x+y+251/52x+y2-81/sqrt5x-2y-141/sqrt52x-y+1=0
- 401/5x-2y^2+361/5x-2y2x+y+251/52x+y^2-81/sqrt5x-2y-141/sqrt52x-y+1=0
- 40*1/5*(x-2*y)^2+36*1/5*(x-2*y)*(2*x+y)+25*1/5*(2*x+y)^2-8*1/sqrt(5)*(x-2*y)-14*1/sqrt(5)*(2*x-y)+1=O
- 40*1 divide by 5*(x-2*y)^2+36*1 divide by 5*(x-2*y)*(2*x+y)+25*1 divide by 5*(2*x+y)^2-8*1 divide by sqrt(5)*(x-2*y)-14*1 divide by sqrt(5)*(2*x-y)+1=0
-
Similar expressions
- 40*1/5*(x-2*y)^2+36*1/5*(x-2*y)*(2*x+y)-25*1/5*(2*x+y)^2-8*1/sqrt(5)*(x-2*y)-14*1/sqrt(5)*(2*x-y)+1=0
- 40*1/5*(x-2*y)^2+36*1/5*(x+2*y)*(2*x+y)+25*1/5*(2*x+y)^2-8*1/sqrt(5)*(x-2*y)-14*1/sqrt(5)*(2*x-y)+1=0
- 40*1/5*(x-2*y)^2+36*1/5*(x-2*y)*(2*x+y)+25*1/5*(2*x+y)^2-8*1/sqrt(5)*(x+2*y)-14*1/sqrt(5)*(2*x-y)+1=0
- 40*1/5*(x-2*y)^2-36*1/5*(x-2*y)*(2*x+y)+25*1/5*(2*x+y)^2-8*1/sqrt(5)*(x-2*y)-14*1/sqrt(5)*(2*x-y)+1=0
- 40*1/5*(x-2*y)^2+36*1/5*(x-2*y)*(2*x+y)+25*1/5*(2*x+y)^2+8*1/sqrt(5)*(x-2*y)-14*1/sqrt(5)*(2*x-y)+1=0
- 40*1/5*(x-2*y)^2+36*1/5*(x-2*y)*(2*x-y)+25*1/5*(2*x+y)^2-8*1/sqrt(5)*(x-2*y)-14*1/sqrt(5)*(2*x-y)+1=0
- 40*1/5*(x-2*y)^2+36*1/5*(x-2*y)*(2*x+y)+25*1/5*(2*x+y)^2-8*1/sqrt(5)*(x-2*y)-14*1/sqrt(5)*(2*x-y)-1=0
- 40*1/5*(x-2*y)^2+36*1/5*(x-2*y)*(2*x+y)+25*1/5*(2*x+y)^2-8*1/sqrt(5)*(x-2*y)-14*1/sqrt(5)*(2*x+y)+1=0
- 40*1/5*(x+2*y)^2+36*1/5*(x-2*y)*(2*x+y)+25*1/5*(2*x+y)^2-8*1/sqrt(5)*(x-2*y)-14*1/sqrt(5)*(2*x-y)+1=0
- 40*1/5*(x-2*y)^2+36*1/5*(x-2*y)*(2*x+y)+25*1/5*(2*x+y)^2-8*1/sqrt(5)*(x-2*y)+14*1/sqrt(5)*(2*x-y)+1=0
- 40*1/5*(x-2*y)^2+36*1/5*(x-2*y)*(2*x+y)+25*1/5*(2*x-y)^2-8*1/sqrt(5)*(x-2*y)-14*1/sqrt(5)*(2*x-y)+1=0
40*1/5*(x-2*y)^2+36*1/5*(x-2*y)*(2*x+y)+25*1/5*(2*x+y)^2-8*1/sqrt(5)*(x-2*y)-14*1/sqrt(5)*(2*x-y)+1=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
40 2 36 25 2 8 14
--*(x - 2*y) + --*(x - 2*y)*(2*x + y) + --*(2*x + y) - -----*(x - 2*y) - -----*(2*x - y) + 1 = 0
5 5 5 ___ ___
\/ 5 \/ 5
$$\left(- \left(2 x - y\right) \frac{14}{\sqrt{5}} + \left(- \left(x - 2 y\right) \frac{8}{\sqrt{5}} + \left(\frac{25}{5} \left(2 x + y\right)^{2} + \left(\frac{40}{5} \left(x - 2 y\right)^{2} + \frac{36}{5} \left(x - 2 y\right) \left(2 x + y\right)\right)\right)\right)\right) + 1 = 0$$
Detail solution
Expand the expression in the equation
$$\left(- \left(2 x - y\right) \frac{14}{\sqrt{5}} + \left(- \left(x - 2 y\right) \frac{8}{\sqrt{5}} + \left(\frac{25}{5} \left(2 x + y\right)^{2} + \left(\frac{40}{5} \left(x - 2 y\right)^{2} + \frac{36}{5} \left(x - 2 y\right) \left(2 x + y\right)\right)\right)\right)\right) + 1 = 0$$
We get the quadratic equation
$$\frac{212 x^{2}}{5} - \frac{168 x y}{5} - \frac{36 \sqrt{5} x}{5} + \frac{113 y^{2}}{5} + 6 \sqrt{5} y + 1 = 0$$
This equation is of the form
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = \frac{212}{5}$$
$$b = - \frac{168 y}{5} - \frac{36 \sqrt{5}}{5}$$
$$c = \frac{113 y^{2}}{5} + 6 \sqrt{5} y + 1$$
, then
The equation has two roots.
or
$$x_{1} = \frac{21 y}{53} + \frac{5 \sqrt{- \frac{95824 y^{2}}{25} - \frac{5088 \sqrt{5} y}{5} + \left(- \frac{168 y}{5} - \frac{36 \sqrt{5}}{5}\right)^{2} - \frac{848}{5}}}{424} + \frac{9 \sqrt{5}}{106}$$
$$x_{2} = \frac{21 y}{53} - \frac{5 \sqrt{- \frac{95824 y^{2}}{25} - \frac{5088 \sqrt{5} y}{5} + \left(- \frac{168 y}{5} - \frac{36 \sqrt{5}}{5}\right)^{2} - \frac{848}{5}}}{424} + \frac{9 \sqrt{5}}{106}$$
$$\left(- \left(2 x - y\right) \frac{14}{\sqrt{5}} + \left(- \left(x - 2 y\right) \frac{8}{\sqrt{5}} + \left(\frac{25}{5} \left(2 x + y\right)^{2} + \left(\frac{40}{5} \left(x - 2 y\right)^{2} + \frac{36}{5} \left(x - 2 y\right) \left(2 x + y\right)\right)\right)\right)\right) + 1 = 0$$
We get the quadratic equation
$$\frac{212 x^{2}}{5} - \frac{168 x y}{5} - \frac{36 \sqrt{5} x}{5} + \frac{113 y^{2}}{5} + 6 \sqrt{5} y + 1 = 0$$
This equation is of the form
a*x^2 + b*x + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = \frac{212}{5}$$
$$b = - \frac{168 y}{5} - \frac{36 \sqrt{5}}{5}$$
$$c = \frac{113 y^{2}}{5} + 6 \sqrt{5} y + 1$$
, then
D = b^2 - 4 * a * c =
(-168*y/5 - 36*sqrt(5)/5)^2 - 4 * (212/5) * (1 + 113*y^2/5 + 6*y*sqrt(5)) = -848/5 + (-168*y/5 - 36*sqrt(5)/5)^2 - 95824*y^2/25 - 5088*y*sqrt(5)/5
The equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{21 y}{53} + \frac{5 \sqrt{- \frac{95824 y^{2}}{25} - \frac{5088 \sqrt{5} y}{5} + \left(- \frac{168 y}{5} - \frac{36 \sqrt{5}}{5}\right)^{2} - \frac{848}{5}}}{424} + \frac{9 \sqrt{5}}{106}$$
$$x_{2} = \frac{21 y}{53} - \frac{5 \sqrt{- \frac{95824 y^{2}}{25} - \frac{5088 \sqrt{5} y}{5} + \left(- \frac{168 y}{5} - \frac{36 \sqrt{5}}{5}\right)^{2} - \frac{848}{5}}}{424} + \frac{9 \sqrt{5}}{106}$$
The graph
Sum and product of roots
[src]
sum
/ _______________________________________________________________________________________________ \ _______________________________________________________________________________________________ / _______________________________________________________________________________________________ \ _______________________________________________________________________________________________
| / 2 2 / / ___ 2 2 ___ \\| / 2 2 / / ___ 2 2 ___ \\ | / 2 2 / / ___ 2 2 ___ \\| / 2 2 / / ___ 2 2 ___ \\
| 4 / / ___ \ / 2 2 ___ \ |atan2\-8450*im(y)*re(y) - 834*\/ 5 *im(y), 140 - 4225*re (y) + 4225*im (y) - 834*\/ 5 *re(y)/|| 4 / / ___ \ / 2 2 ___ \ |atan2\-8450*im(y)*re(y) - 834*\/ 5 *im(y), 140 - 4225*re (y) + 4225*im (y) - 834*\/ 5 *re(y)/| | 4 / / ___ \ / 2 2 ___ \ |atan2\-8450*im(y)*re(y) - 834*\/ 5 *im(y), 140 - 4225*re (y) + 4225*im (y) - 834*\/ 5 *re(y)/|| 4 / / ___ \ / 2 2 ___ \ |atan2\-8450*im(y)*re(y) - 834*\/ 5 *im(y), 140 - 4225*re (y) + 4225*im (y) - 834*\/ 5 *re(y)/|
___ | \/ \-8450*im(y)*re(y) - 834*\/ 5 *im(y)/ + \140 - 4225*re (y) + 4225*im (y) - 834*\/ 5 *re(y)/ *sin|---------------------------------------------------------------------------------------------|| \/ \-8450*im(y)*re(y) - 834*\/ 5 *im(y)/ + \140 - 4225*re (y) + 4225*im (y) - 834*\/ 5 *re(y)/ *cos|---------------------------------------------------------------------------------------------| ___ | \/ \-8450*im(y)*re(y) - 834*\/ 5 *im(y)/ + \140 - 4225*re (y) + 4225*im (y) - 834*\/ 5 *re(y)/ *sin|---------------------------------------------------------------------------------------------|| \/ \-8450*im(y)*re(y) - 834*\/ 5 *im(y)/ + \140 - 4225*re (y) + 4225*im (y) - 834*\/ 5 *re(y)/ *cos|---------------------------------------------------------------------------------------------|
9*\/ 5 21*re(y) |21*im(y) \ 2 /| \ 2 / 9*\/ 5 21*re(y) |21*im(y) \ 2 /| \ 2 /
------- + -------- + I*|-------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + ------- + -------- + I*|-------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
106 53 \ 53 106 / 106 106 53 \ 53 106 / 106
$$\left(i \left(- \frac{\sqrt[4]{\left(- 8450 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 834 \sqrt{5} \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 4225 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 834 \sqrt{5} \operatorname{re}{\left(y\right)} + 4225 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 140\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 8450 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 834 \sqrt{5} \operatorname{im}{\left(y\right)},- 4225 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 834 \sqrt{5} \operatorname{re}{\left(y\right)} + 4225 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 140 \right)}}{2} \right)}}{106} + \frac{21 \operatorname{im}{\left(y\right)}}{53}\right) - \frac{\sqrt[4]{\left(- 8450 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 834 \sqrt{5} \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 4225 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 834 \sqrt{5} \operatorname{re}{\left(y\right)} + 4225 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 140\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 8450 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 834 \sqrt{5} \operatorname{im}{\left(y\right)},- 4225 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 834 \sqrt{5} \operatorname{re}{\left(y\right)} + 4225 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 140 \right)}}{2} \right)}}{106} + \frac{21 \operatorname{re}{\left(y\right)}}{53} + \frac{9 \sqrt{5}}{106}\right) + \left(i \left(\frac{\sqrt[4]{\left(- 8450 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 834 \sqrt{5} \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 4225 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 834 \sqrt{5} \operatorname{re}{\left(y\right)} + 4225 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 140\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 8450 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 834 \sqrt{5} \operatorname{im}{\left(y\right)},- 4225 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 834 \sqrt{5} \operatorname{re}{\left(y\right)} + 4225 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 140 \right)}}{2} \right)}}{106} + \frac{21 \operatorname{im}{\left(y\right)}}{53}\right) + \frac{\sqrt[4]{\left(- 8450 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 834 \sqrt{5} \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 4225 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 834 \sqrt{5} \operatorname{re}{\left(y\right)} + 4225 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 140\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 8450 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 834 \sqrt{5} \operatorname{im}{\left(y\right)},- 4225 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 834 \sqrt{5} \operatorname{re}{\left(y\right)} + 4225 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 140 \right)}}{2} \right)}}{106} + \frac{21 \operatorname{re}{\left(y\right)}}{53} + \frac{9 \sqrt{5}}{106}\right)$$
=
/ _______________________________________________________________________________________________ \ / _______________________________________________________________________________________________ \
| / 2 2 / / ___ 2 2 ___ \\| | / 2 2 / / ___ 2 2 ___ \\|
| 4 / / ___ \ / 2 2 ___ \ |atan2\-8450*im(y)*re(y) - 834*\/ 5 *im(y), 140 - 4225*re (y) + 4225*im (y) - 834*\/ 5 *re(y)/|| | 4 / / ___ \ / 2 2 ___ \ |atan2\-8450*im(y)*re(y) - 834*\/ 5 *im(y), 140 - 4225*re (y) + 4225*im (y) - 834*\/ 5 *re(y)/||
___ | \/ \-8450*im(y)*re(y) - 834*\/ 5 *im(y)/ + \140 - 4225*re (y) + 4225*im (y) - 834*\/ 5 *re(y)/ *sin|---------------------------------------------------------------------------------------------|| | \/ \-8450*im(y)*re(y) - 834*\/ 5 *im(y)/ + \140 - 4225*re (y) + 4225*im (y) - 834*\/ 5 *re(y)/ *sin|---------------------------------------------------------------------------------------------||
9*\/ 5 42*re(y) |21*im(y) \ 2 /| |21*im(y) \ 2 /|
------- + -------- + I*|-------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + I*|-------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
53 53 \ 53 106 / \ 53 106 /
$$i \left(- \frac{\sqrt[4]{\left(- 8450 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 834 \sqrt{5} \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 4225 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 834 \sqrt{5} \operatorname{re}{\left(y\right)} + 4225 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 140\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 8450 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 834 \sqrt{5} \operatorname{im}{\left(y\right)},- 4225 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 834 \sqrt{5} \operatorname{re}{\left(y\right)} + 4225 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 140 \right)}}{2} \right)}}{106} + \frac{21 \operatorname{im}{\left(y\right)}}{53}\right) + i \left(\frac{\sqrt[4]{\left(- 8450 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 834 \sqrt{5} \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 4225 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 834 \sqrt{5} \operatorname{re}{\left(y\right)} + 4225 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 140\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 8450 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 834 \sqrt{5} \operatorname{im}{\left(y\right)},- 4225 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 834 \sqrt{5} \operatorname{re}{\left(y\right)} + 4225 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 140 \right)}}{2} \right)}}{106} + \frac{21 \operatorname{im}{\left(y\right)}}{53}\right) + \frac{42 \operatorname{re}{\left(y\right)}}{53} + \frac{9 \sqrt{5}}{53}$$
product
/ / _______________________________________________________________________________________________ \ _______________________________________________________________________________________________ \ / / _______________________________________________________________________________________________ \ _______________________________________________________________________________________________ \ | | / 2 2 / / ___ 2 2 ___ \\| / 2 2 / / ___ 2 2 ___ \\| | | / 2 2 / / ___ 2 2 ___ \\| / 2 2 / / ___ 2 2 ___ \\| | | 4 / / ___ \ / 2 2 ___ \ |atan2\-8450*im(y)*re(y) - 834*\/ 5 *im(y), 140 - 4225*re (y) + 4225*im (y) - 834*\/ 5 *re(y)/|| 4 / / ___ \ / 2 2 ___ \ |atan2\-8450*im(y)*re(y) - 834*\/ 5 *im(y), 140 - 4225*re (y) + 4225*im (y) - 834*\/ 5 *re(y)/|| | | 4 / / ___ \ / 2 2 ___ \ |atan2\-8450*im(y)*re(y) - 834*\/ 5 *im(y), 140 - 4225*re (y) + 4225*im (y) - 834*\/ 5 *re(y)/|| 4 / / ___ \ / 2 2 ___ \ |atan2\-8450*im(y)*re(y) - 834*\/ 5 *im(y), 140 - 4225*re (y) + 4225*im (y) - 834*\/ 5 *re(y)/|| | ___ | \/ \-8450*im(y)*re(y) - 834*\/ 5 *im(y)/ + \140 - 4225*re (y) + 4225*im (y) - 834*\/ 5 *re(y)/ *sin|---------------------------------------------------------------------------------------------|| \/ \-8450*im(y)*re(y) - 834*\/ 5 *im(y)/ + \140 - 4225*re (y) + 4225*im (y) - 834*\/ 5 *re(y)/ *cos|---------------------------------------------------------------------------------------------|| | ___ | \/ \-8450*im(y)*re(y) - 834*\/ 5 *im(y)/ + \140 - 4225*re (y) + 4225*im (y) - 834*\/ 5 *re(y)/ *sin|---------------------------------------------------------------------------------------------|| \/ \-8450*im(y)*re(y) - 834*\/ 5 *im(y)/ + \140 - 4225*re (y) + 4225*im (y) - 834*\/ 5 *re(y)/ *cos|---------------------------------------------------------------------------------------------|| |9*\/ 5 21*re(y) |21*im(y) \ 2 /| \ 2 /| |9*\/ 5 21*re(y) |21*im(y) \ 2 /| \ 2 /| |------- + -------- + I*|-------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|------- + -------- + I*|-------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| \ 106 53 \ 53 106 / 106 / \ 106 53 \ 53 106 / 106 /
$$\left(i \left(- \frac{\sqrt[4]{\left(- 8450 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 834 \sqrt{5} \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 4225 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 834 \sqrt{5} \operatorname{re}{\left(y\right)} + 4225 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 140\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 8450 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 834 \sqrt{5} \operatorname{im}{\left(y\right)},- 4225 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 834 \sqrt{5} \operatorname{re}{\left(y\right)} + 4225 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 140 \right)}}{2} \right)}}{106} + \frac{21 \operatorname{im}{\left(y\right)}}{53}\right) - \frac{\sqrt[4]{\left(- 8450 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 834 \sqrt{5} \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 4225 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 834 \sqrt{5} \operatorname{re}{\left(y\right)} + 4225 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 140\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 8450 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 834 \sqrt{5} \operatorname{im}{\left(y\right)},- 4225 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 834 \sqrt{5} \operatorname{re}{\left(y\right)} + 4225 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 140 \right)}}{2} \right)}}{106} + \frac{21 \operatorname{re}{\left(y\right)}}{53} + \frac{9 \sqrt{5}}{106}\right) \left(i \left(\frac{\sqrt[4]{\left(- 8450 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 834 \sqrt{5} \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 4225 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 834 \sqrt{5} \operatorname{re}{\left(y\right)} + 4225 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 140\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 8450 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 834 \sqrt{5} \operatorname{im}{\left(y\right)},- 4225 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 834 \sqrt{5} \operatorname{re}{\left(y\right)} + 4225 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 140 \right)}}{2} \right)}}{106} + \frac{21 \operatorname{im}{\left(y\right)}}{53}\right) + \frac{\sqrt[4]{\left(- 8450 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 834 \sqrt{5} \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 4225 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 834 \sqrt{5} \operatorname{re}{\left(y\right)} + 4225 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 140\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 8450 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 834 \sqrt{5} \operatorname{im}{\left(y\right)},- 4225 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 834 \sqrt{5} \operatorname{re}{\left(y\right)} + 4225 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 140 \right)}}{2} \right)}}{106} + \frac{21 \operatorname{re}{\left(y\right)}}{53} + \frac{9 \sqrt{5}}{106}\right)$$
=
/ / _______________________________________________________________________________________________ \ _______________________________________________________________________________________________ \ / / _______________________________________________________________________________________________ \ _______________________________________________________________________________________________ \ | | / 2 2 / / ___ 2 2 ___ \\| / 2 2 / / ___ 2 2 ___ \\| | | / 2 2 / / ___ 2 2 ___ \\| / 2 2 / / ___ 2 2 ___ \\| | | 4 / / ___ \ / 2 2 ___ \ |atan2\-8450*im(y)*re(y) - 834*\/ 5 *im(y), 140 - 4225*re (y) + 4225*im (y) - 834*\/ 5 *re(y)/|| 4 / / ___ \ / 2 2 ___ \ |atan2\-8450*im(y)*re(y) - 834*\/ 5 *im(y), 140 - 4225*re (y) + 4225*im (y) - 834*\/ 5 *re(y)/|| | | 4 / / ___ \ / 2 2 ___ \ |atan2\-8450*im(y)*re(y) - 834*\/ 5 *im(y), 140 - 4225*re (y) + 4225*im (y) - 834*\/ 5 *re(y)/|| 4 / / ___ \ / 2 2 ___ \ |atan2\-8450*im(y)*re(y) - 834*\/ 5 *im(y), 140 - 4225*re (y) + 4225*im (y) - 834*\/ 5 *re(y)/|| | ___ | \/ \-8450*im(y)*re(y) - 834*\/ 5 *im(y)/ + \140 - 4225*re (y) + 4225*im (y) - 834*\/ 5 *re(y)/ *sin|---------------------------------------------------------------------------------------------|| \/ \834*\/ 5 *im(y) + 8450*im(y)*re(y)/ + \-140 - 4225*im (y) + 4225*re (y) + 834*\/ 5 *re(y)/ *cos|---------------------------------------------------------------------------------------------|| | ___ | \/ \834*\/ 5 *im(y) + 8450*im(y)*re(y)/ + \-140 - 4225*im (y) + 4225*re (y) + 834*\/ 5 *re(y)/ *sin|---------------------------------------------------------------------------------------------|| \/ \834*\/ 5 *im(y) + 8450*im(y)*re(y)/ + \-140 - 4225*im (y) + 4225*re (y) + 834*\/ 5 *re(y)/ *cos|---------------------------------------------------------------------------------------------|| | 21*re(y) 9*\/ 5 | 21*im(y) \ 2 /| \ 2 /| |9*\/ 5 21*re(y) |21*im(y) \ 2 /| \ 2 /| -|- -------- - ------- + I*|- -------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|------- + -------- + I*|-------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| \ 53 106 \ 53 106 / 106 / \ 106 53 \ 53 106 / 106 /
$$- \left(i \left(\frac{\sqrt[4]{\left(- 8450 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 834 \sqrt{5} \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 4225 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 834 \sqrt{5} \operatorname{re}{\left(y\right)} + 4225 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 140\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 8450 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 834 \sqrt{5} \operatorname{im}{\left(y\right)},- 4225 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 834 \sqrt{5} \operatorname{re}{\left(y\right)} + 4225 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 140 \right)}}{2} \right)}}{106} - \frac{21 \operatorname{im}{\left(y\right)}}{53}\right) + \frac{\sqrt[4]{\left(8450 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 834 \sqrt{5} \operatorname{im}{\left(y\right)}\right)^{2} + \left(4225 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 834 \sqrt{5} \operatorname{re}{\left(y\right)} - 4225 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 140\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 8450 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 834 \sqrt{5} \operatorname{im}{\left(y\right)},- 4225 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 834 \sqrt{5} \operatorname{re}{\left(y\right)} + 4225 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 140 \right)}}{2} \right)}}{106} - \frac{21 \operatorname{re}{\left(y\right)}}{53} - \frac{9 \sqrt{5}}{106}\right) \left(i \left(\frac{\sqrt[4]{\left(8450 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 834 \sqrt{5} \operatorname{im}{\left(y\right)}\right)^{2} + \left(4225 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 834 \sqrt{5} \operatorname{re}{\left(y\right)} - 4225 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 140\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 8450 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 834 \sqrt{5} \operatorname{im}{\left(y\right)},- 4225 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 834 \sqrt{5} \operatorname{re}{\left(y\right)} + 4225 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 140 \right)}}{2} \right)}}{106} + \frac{21 \operatorname{im}{\left(y\right)}}{53}\right) + \frac{\sqrt[4]{\left(8450 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 834 \sqrt{5} \operatorname{im}{\left(y\right)}\right)^{2} + \left(4225 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 834 \sqrt{5} \operatorname{re}{\left(y\right)} - 4225 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 140\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 8450 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 834 \sqrt{5} \operatorname{im}{\left(y\right)},- 4225 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 834 \sqrt{5} \operatorname{re}{\left(y\right)} + 4225 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 140 \right)}}{2} \right)}}{106} + \frac{21 \operatorname{re}{\left(y\right)}}{53} + \frac{9 \sqrt{5}}{106}\right)$$
-(-21*re(y)/53 - 9*sqrt(5)/106 + i*(-21*im(y)/53 + ((-8450*im(y)*re(y) - 834*sqrt(5)*im(y))^2 + (140 - 4225*re(y)^2 + 4225*im(y)^2 - 834*sqrt(5)*re(y))^2)^(1/4)*sin(atan2(-8450*im(y)*re(y) - 834*sqrt(5)*im(y), 140 - 4225*re(y)^2 + 4225*im(y)^2 - 834*sqrt(5)*re(y))/2)/106) + ((834*sqrt(5)*im(y) + 8450*im(y)*re(y))^2 + (-140 - 4225*im(y)^2 + 4225*re(y)^2 + 834*sqrt(5)*re(y))^2)^(1/4)*cos(atan2(-8450*im(y)*re(y) - 834*sqrt(5)*im(y), 140 - 4225*re(y)^2 + 4225*im(y)^2 - 834*sqrt(5)*re(y))/2)/106)*(9*sqrt(5)/106 + 21*re(y)/53 + i*(21*im(y)/53 + ((834*sqrt(5)*im(y) + 8450*im(y)*re(y))^2 + (-140 - 4225*im(y)^2 + 4225*re(y)^2 + 834*sqrt(5)*re(y))^2)^(1/4)*sin(atan2(-8450*im(y)*re(y) - 834*sqrt(5)*im(y), 140 - 4225*re(y)^2 + 4225*im(y)^2 - 834*sqrt(5)*re(y))/2)/106) + ((834*sqrt(5)*im(y) + 8450*im(y)*re(y))^2 + (-140 - 4225*im(y)^2 + 4225*re(y)^2 + 834*sqrt(5)*re(y))^2)^(1/4)*cos(atan2(-8450*im(y)*re(y) - 834*sqrt(5)*im(y), 140 - 4225*re(y)^2 + 4225*im(y)^2 - 834*sqrt(5)*re(y))/2)/106)
Rapid solution
[src]
/ _______________________________________________________________________________________________ \ _______________________________________________________________________________________________
| / 2 2 / / ___ 2 2 ___ \\| / 2 2 / / ___ 2 2 ___ \\
| 4 / / ___ \ / 2 2 ___ \ |atan2\-8450*im(y)*re(y) - 834*\/ 5 *im(y), 140 - 4225*re (y) + 4225*im (y) - 834*\/ 5 *re(y)/|| 4 / / ___ \ / 2 2 ___ \ |atan2\-8450*im(y)*re(y) - 834*\/ 5 *im(y), 140 - 4225*re (y) + 4225*im (y) - 834*\/ 5 *re(y)/|
___ | \/ \-8450*im(y)*re(y) - 834*\/ 5 *im(y)/ + \140 - 4225*re (y) + 4225*im (y) - 834*\/ 5 *re(y)/ *sin|---------------------------------------------------------------------------------------------|| \/ \-8450*im(y)*re(y) - 834*\/ 5 *im(y)/ + \140 - 4225*re (y) + 4225*im (y) - 834*\/ 5 *re(y)/ *cos|---------------------------------------------------------------------------------------------|
9*\/ 5 21*re(y) |21*im(y) \ 2 /| \ 2 /
x1 = ------- + -------- + I*|-------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
106 53 \ 53 106 / 106
$$x_{1} = i \left(- \frac{\sqrt[4]{\left(- 8450 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 834 \sqrt{5} \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 4225 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 834 \sqrt{5} \operatorname{re}{\left(y\right)} + 4225 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 140\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 8450 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 834 \sqrt{5} \operatorname{im}{\left(y\right)},- 4225 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 834 \sqrt{5} \operatorname{re}{\left(y\right)} + 4225 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 140 \right)}}{2} \right)}}{106} + \frac{21 \operatorname{im}{\left(y\right)}}{53}\right) - \frac{\sqrt[4]{\left(- 8450 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 834 \sqrt{5} \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 4225 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 834 \sqrt{5} \operatorname{re}{\left(y\right)} + 4225 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 140\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 8450 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 834 \sqrt{5} \operatorname{im}{\left(y\right)},- 4225 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 834 \sqrt{5} \operatorname{re}{\left(y\right)} + 4225 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 140 \right)}}{2} \right)}}{106} + \frac{21 \operatorname{re}{\left(y\right)}}{53} + \frac{9 \sqrt{5}}{106}$$
/ _______________________________________________________________________________________________ \ _______________________________________________________________________________________________
| / 2 2 / / ___ 2 2 ___ \\| / 2 2 / / ___ 2 2 ___ \\
| 4 / / ___ \ / 2 2 ___ \ |atan2\-8450*im(y)*re(y) - 834*\/ 5 *im(y), 140 - 4225*re (y) + 4225*im (y) - 834*\/ 5 *re(y)/|| 4 / / ___ \ / 2 2 ___ \ |atan2\-8450*im(y)*re(y) - 834*\/ 5 *im(y), 140 - 4225*re (y) + 4225*im (y) - 834*\/ 5 *re(y)/|
___ | \/ \-8450*im(y)*re(y) - 834*\/ 5 *im(y)/ + \140 - 4225*re (y) + 4225*im (y) - 834*\/ 5 *re(y)/ *sin|---------------------------------------------------------------------------------------------|| \/ \-8450*im(y)*re(y) - 834*\/ 5 *im(y)/ + \140 - 4225*re (y) + 4225*im (y) - 834*\/ 5 *re(y)/ *cos|---------------------------------------------------------------------------------------------|
9*\/ 5 21*re(y) |21*im(y) \ 2 /| \ 2 /
x2 = ------- + -------- + I*|-------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
106 53 \ 53 106 / 106
$$x_{2} = i \left(\frac{\sqrt[4]{\left(- 8450 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 834 \sqrt{5} \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 4225 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 834 \sqrt{5} \operatorname{re}{\left(y\right)} + 4225 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 140\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 8450 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 834 \sqrt{5} \operatorname{im}{\left(y\right)},- 4225 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 834 \sqrt{5} \operatorname{re}{\left(y\right)} + 4225 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 140 \right)}}{2} \right)}}{106} + \frac{21 \operatorname{im}{\left(y\right)}}{53}\right) + \frac{\sqrt[4]{\left(- 8450 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 834 \sqrt{5} \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 4225 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 834 \sqrt{5} \operatorname{re}{\left(y\right)} + 4225 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 140\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 8450 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 834 \sqrt{5} \operatorname{im}{\left(y\right)},- 4225 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 834 \sqrt{5} \operatorname{re}{\left(y\right)} + 4225 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 140 \right)}}{2} \right)}}{106} + \frac{21 \operatorname{re}{\left(y\right)}}{53} + \frac{9 \sqrt{5}}{106}$$
x2 = i*(((-8450*re(y)*im(y) - 834*sqrt(5)*im(y))^2 + (-4225*re(y)^2 - 834*sqrt(5)*re(y) + 4225*im(y)^2 + 140)^2)^(1/4)*sin(atan2(-8450*re(y)*im(y) - 834*sqrt(5)*im(y, -4225*re(y)^2 - 834*sqrt(5)*re(y) + 4225*im(y)^2 + 140)/2)/106 + 21*im(y)/53) + ((-8450*re(y)*im(y) - 834*sqrt(5)*im(y))^2 + (-4225*re(y)^2 - 834*sqrt(5)*re(y) + 4225*im(y)^2 + 140)^2)^(1/4)*cos(atan2(-8450*re(y)*im(y) - 834*sqrt(5)*im(y), -4225*re(y)^2 - 834*sqrt(5)*re(y) + 4225*im(y)^2 + 140)/2)/106 + 21*re(y)/53 + 9*sqrt(5)/106)