Mister Exam
Other calculators
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How to use it?
- Equation:
- Equation (a-2)(b+5)=(a-2)b+(a-2)5
-
Equation x^2-x-7=0
- Equation (x^2+a)/x+x/(x^2+a)=-5/2
-
Equation x^2-6x+13=0
- Express {x} in terms of y where:
- -8*x-2*y=-11
- 19*x-20*y=-7
- -3*x+1*y=3
- -5*x-20*y=-3
- Limit of the function:
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-5/2
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Identical expressions
- (x^ two +a)/x+x/(x^ two +a)=- five / two
- (x squared plus a) divide by x plus x divide by (x squared plus a) equally minus 5 divide by 2
- (x to the power of two plus a) divide by x plus x divide by (x to the power of two plus a) equally minus five divide by two
- (x2+a)/x+x/(x2+a)=-5/2
- x2+a/x+x/x2+a=-5/2
- (x²+a)/x+x/(x²+a)=-5/2
- (x to the power of 2+a)/x+x/(x to the power of 2+a)=-5/2
- x^2+a/x+x/x^2+a=-5/2
- (x^2+a) divide by x+x divide by (x^2+a)=-5 divide by 2
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Similar expressions
- (x^2-a)/x+x/(x^2+a)=-5/2
- (|2*x+3|-5)/(2*x^2+11*x+12)=0
- (x^2+a)/x-x/(x^2+a)=-5/2
- -(26/5)+x=-(5/2)
- (x^2+a)/x+x/(x^2-a)=-5/2
- (sqrt(5)-(5/2))*(3-2*x)=0
- (x^2+a)/x+x/(x^2+a)=+5/2
(x^2+a)/x+x/(x^2+a)=-5/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
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[src]
2
x + a x
------ + ------ = -5/2
x 2
x + a
$$\frac{x}{a + x^{2}} + \frac{a + x^{2}}{x} = - \frac{5}{2}$$
The graph
Rapid solution
[src]
______________________________ ______________________________
4 / 2 2 /atan2(-16*im(a), 1 - 16*re(a))\ 4 / 2 2 /atan2(-16*im(a), 1 - 16*re(a))\
\/ (1 - 16*re(a)) + 256*im (a) *cos|------------------------------| I*\/ (1 - 16*re(a)) + 256*im (a) *sin|------------------------------|
1 \ 2 / \ 2 /
x1 = - - - --------------------------------------------------------------------- - -----------------------------------------------------------------------
4 4 4
$$x_{1} = - \frac{i \sqrt[4]{\left(1 - 16 \operatorname{re}{\left(a\right)}\right)^{2} + 256 \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{im}{\left(a\right)},1 - 16 \operatorname{re}{\left(a\right)} \right)}}{2} \right)}}{4} - \frac{\sqrt[4]{\left(1 - 16 \operatorname{re}{\left(a\right)}\right)^{2} + 256 \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{im}{\left(a\right)},1 - 16 \operatorname{re}{\left(a\right)} \right)}}{2} \right)}}{4} - \frac{1}{4}$$
______________________________ ______________________________
4 / 2 2 /atan2(-16*im(a), 1 - 16*re(a))\ 4 / 2 2 /atan2(-16*im(a), 1 - 16*re(a))\
\/ (1 - 16*re(a)) + 256*im (a) *cos|------------------------------| I*\/ (1 - 16*re(a)) + 256*im (a) *sin|------------------------------|
1 \ 2 / \ 2 /
x2 = - - + --------------------------------------------------------------------- + -----------------------------------------------------------------------
4 4 4
$$x_{2} = \frac{i \sqrt[4]{\left(1 - 16 \operatorname{re}{\left(a\right)}\right)^{2} + 256 \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{im}{\left(a\right)},1 - 16 \operatorname{re}{\left(a\right)} \right)}}{2} \right)}}{4} + \frac{\sqrt[4]{\left(1 - 16 \operatorname{re}{\left(a\right)}\right)^{2} + 256 \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{im}{\left(a\right)},1 - 16 \operatorname{re}{\left(a\right)} \right)}}{2} \right)}}{4} - \frac{1}{4}$$
_______________________ _______________________
4 / 2 2 /atan2(-im(a), 1 - re(a))\ 4 / 2 2 /atan2(-im(a), 1 - re(a))\
x3 = -1 - \/ (1 - re(a)) + im (a) *cos|------------------------| - I*\/ (1 - re(a)) + im (a) *sin|------------------------|
\ 2 / \ 2 /
$$x_{3} = - i \sqrt[4]{\left(1 - \operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(a\right)},1 - \operatorname{re}{\left(a\right)} \right)}}{2} \right)} - \sqrt[4]{\left(1 - \operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(a\right)},1 - \operatorname{re}{\left(a\right)} \right)}}{2} \right)} - 1$$
_______________________ _______________________
4 / 2 2 /atan2(-im(a), 1 - re(a))\ 4 / 2 2 /atan2(-im(a), 1 - re(a))\
x4 = -1 + \/ (1 - re(a)) + im (a) *cos|------------------------| + I*\/ (1 - re(a)) + im (a) *sin|------------------------|
\ 2 / \ 2 /
$$x_{4} = i \sqrt[4]{\left(1 - \operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(a\right)},1 - \operatorname{re}{\left(a\right)} \right)}}{2} \right)} + \sqrt[4]{\left(1 - \operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(a\right)},1 - \operatorname{re}{\left(a\right)} \right)}}{2} \right)} - 1$$
x4 = i*((1 - re(a))^2 + im(a)^2)^(1/4)*sin(atan2(-im(a, 1 - re(a))/2) + ((1 - re(a))^2 + im(a)^2)^(1/4)*cos(atan2(-im(a), 1 - re(a))/2) - 1)
Sum and product of roots
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sum
______________________________ ______________________________ ______________________________ ______________________________
4 / 2 2 /atan2(-16*im(a), 1 - 16*re(a))\ 4 / 2 2 /atan2(-16*im(a), 1 - 16*re(a))\ 4 / 2 2 /atan2(-16*im(a), 1 - 16*re(a))\ 4 / 2 2 /atan2(-16*im(a), 1 - 16*re(a))\
\/ (1 - 16*re(a)) + 256*im (a) *cos|------------------------------| I*\/ (1 - 16*re(a)) + 256*im (a) *sin|------------------------------| \/ (1 - 16*re(a)) + 256*im (a) *cos|------------------------------| I*\/ (1 - 16*re(a)) + 256*im (a) *sin|------------------------------| _______________________ _______________________ _______________________ _______________________
1 \ 2 / \ 2 / 1 \ 2 / \ 2 / 4 / 2 2 /atan2(-im(a), 1 - re(a))\ 4 / 2 2 /atan2(-im(a), 1 - re(a))\ 4 / 2 2 /atan2(-im(a), 1 - re(a))\ 4 / 2 2 /atan2(-im(a), 1 - re(a))\
- - - --------------------------------------------------------------------- - ----------------------------------------------------------------------- + - - + --------------------------------------------------------------------- + ----------------------------------------------------------------------- + -1 - \/ (1 - re(a)) + im (a) *cos|------------------------| - I*\/ (1 - re(a)) + im (a) *sin|------------------------| + -1 + \/ (1 - re(a)) + im (a) *cos|------------------------| + I*\/ (1 - re(a)) + im (a) *sin|------------------------|
4 4 4 4 4 4 \ 2 / \ 2 / \ 2 / \ 2 /
$$\left(\left(\left(- \frac{i \sqrt[4]{\left(1 - 16 \operatorname{re}{\left(a\right)}\right)^{2} + 256 \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{im}{\left(a\right)},1 - 16 \operatorname{re}{\left(a\right)} \right)}}{2} \right)}}{4} - \frac{\sqrt[4]{\left(1 - 16 \operatorname{re}{\left(a\right)}\right)^{2} + 256 \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{im}{\left(a\right)},1 - 16 \operatorname{re}{\left(a\right)} \right)}}{2} \right)}}{4} - \frac{1}{4}\right) + \left(\frac{i \sqrt[4]{\left(1 - 16 \operatorname{re}{\left(a\right)}\right)^{2} + 256 \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{im}{\left(a\right)},1 - 16 \operatorname{re}{\left(a\right)} \right)}}{2} \right)}}{4} + \frac{\sqrt[4]{\left(1 - 16 \operatorname{re}{\left(a\right)}\right)^{2} + 256 \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{im}{\left(a\right)},1 - 16 \operatorname{re}{\left(a\right)} \right)}}{2} \right)}}{4} - \frac{1}{4}\right)\right) + \left(- i \sqrt[4]{\left(1 - \operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(a\right)},1 - \operatorname{re}{\left(a\right)} \right)}}{2} \right)} - \sqrt[4]{\left(1 - \operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(a\right)},1 - \operatorname{re}{\left(a\right)} \right)}}{2} \right)} - 1\right)\right) + \left(i \sqrt[4]{\left(1 - \operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(a\right)},1 - \operatorname{re}{\left(a\right)} \right)}}{2} \right)} + \sqrt[4]{\left(1 - \operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(a\right)},1 - \operatorname{re}{\left(a\right)} \right)}}{2} \right)} - 1\right)$$
=
-5/2
$$- \frac{5}{2}$$
product
/ ______________________________ ______________________________ \ / ______________________________ ______________________________ \ | 4 / 2 2 /atan2(-16*im(a), 1 - 16*re(a))\ 4 / 2 2 /atan2(-16*im(a), 1 - 16*re(a))\| | 4 / 2 2 /atan2(-16*im(a), 1 - 16*re(a))\ 4 / 2 2 /atan2(-16*im(a), 1 - 16*re(a))\| | \/ (1 - 16*re(a)) + 256*im (a) *cos|------------------------------| I*\/ (1 - 16*re(a)) + 256*im (a) *sin|------------------------------|| | \/ (1 - 16*re(a)) + 256*im (a) *cos|------------------------------| I*\/ (1 - 16*re(a)) + 256*im (a) *sin|------------------------------|| / _______________________ _______________________ \ / _______________________ _______________________ \ | 1 \ 2 / \ 2 /| | 1 \ 2 / \ 2 /| | 4 / 2 2 /atan2(-im(a), 1 - re(a))\ 4 / 2 2 /atan2(-im(a), 1 - re(a))\| | 4 / 2 2 /atan2(-im(a), 1 - re(a))\ 4 / 2 2 /atan2(-im(a), 1 - re(a))\| |- - - --------------------------------------------------------------------- - -----------------------------------------------------------------------|*|- - + --------------------------------------------------------------------- + -----------------------------------------------------------------------|*|-1 - \/ (1 - re(a)) + im (a) *cos|------------------------| - I*\/ (1 - re(a)) + im (a) *sin|------------------------||*|-1 + \/ (1 - re(a)) + im (a) *cos|------------------------| + I*\/ (1 - re(a)) + im (a) *sin|------------------------|| \ 4 4 4 / \ 4 4 4 / \ \ 2 / \ 2 // \ \ 2 / \ 2 //
$$\left(- \frac{i \sqrt[4]{\left(1 - 16 \operatorname{re}{\left(a\right)}\right)^{2} + 256 \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{im}{\left(a\right)},1 - 16 \operatorname{re}{\left(a\right)} \right)}}{2} \right)}}{4} - \frac{\sqrt[4]{\left(1 - 16 \operatorname{re}{\left(a\right)}\right)^{2} + 256 \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{im}{\left(a\right)},1 - 16 \operatorname{re}{\left(a\right)} \right)}}{2} \right)}}{4} - \frac{1}{4}\right) \left(\frac{i \sqrt[4]{\left(1 - 16 \operatorname{re}{\left(a\right)}\right)^{2} + 256 \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{im}{\left(a\right)},1 - 16 \operatorname{re}{\left(a\right)} \right)}}{2} \right)}}{4} + \frac{\sqrt[4]{\left(1 - 16 \operatorname{re}{\left(a\right)}\right)^{2} + 256 \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{im}{\left(a\right)},1 - 16 \operatorname{re}{\left(a\right)} \right)}}{2} \right)}}{4} - \frac{1}{4}\right) \left(- i \sqrt[4]{\left(1 - \operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(a\right)},1 - \operatorname{re}{\left(a\right)} \right)}}{2} \right)} - \sqrt[4]{\left(1 - \operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(a\right)},1 - \operatorname{re}{\left(a\right)} \right)}}{2} \right)} - 1\right) \left(i \sqrt[4]{\left(1 - \operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(a\right)},1 - \operatorname{re}{\left(a\right)} \right)}}{2} \right)} + \sqrt[4]{\left(1 - \operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(a\right)},1 - \operatorname{re}{\left(a\right)} \right)}}{2} \right)} - 1\right)$$
=
2 2 re (a) - im (a) + 2*I*im(a)*re(a)
$$\left(\operatorname{re}{\left(a\right)}\right)^{2} + 2 i \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}$$
re(a)^2 - im(a)^2 + 2*i*im(a)*re(a)