Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation (x+3)^4-4(x+3)^2-5=0
-
Equation 2x^2-x-3=0
-
Equation 9x-4x+39=94
-
Equation 2(8x-7)=18-4(5-4x)
- Express {x} in terms of y where:
- a^2*(2*x+3*y)=0
- a*x^5-b*x^3*y^2-c*x^2*y^3+d*y^5=0
- (x+7)/(x^2-2*x+3)=y
- sin(3x)^2*sqrt(16-x^2)=y
-
Identical expressions
- u= two *i*n*z*(x^(thirteen / ten)+ three *y)
- u equally 2 multiply by i multiply by n multiply by z multiply by (x to the power of (13 divide by 10) plus 3 multiply by y)
- u equally two multiply by i multiply by n multiply by z multiply by (x to the power of (thirteen divide by ten) plus three multiply by y)
- u=2*i*n*z*(x(13/10)+3*y)
- u=2*i*n*z*x13/10+3*y
- u=2inz(x^(13/10)+3y)
- u=2inz(x(13/10)+3y)
- u=2inzx13/10+3y
- u=2inzx^13/10+3y
- u=2*i*n*z*(x^(13 divide by 10)+3*y)
-
Similar expressions
- u=2*i*n*z*(x^(13/10)-3*y)
u=2*i*n*z*(x^(13/10)+3*y) equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
/ 13 \
| -- |
| 10 |
u = 2*I*n*z*\x + 3*y/
$$u = z 2 i n \left(x^{\frac{13}{10}} + 3 y\right)$$
The solution of the parametric equation
Given the equation with a parameter:
$$u = 2 i n z \left(x^{\frac{13}{10}} + 3 y\right)$$
Коэффициент при z равен
$$- 2 i n \left(x^{\frac{13}{10}} + 3 y\right)$$
then possible cases for n :
$$n < 0$$
$$n = 0$$
Consider all cases in more detail:
With
$$n < 0$$
the equation
$$u + 2 i z \left(x^{\frac{13}{10}} + 3 y\right) = 0$$
its solution
$$z = \frac{i u}{2 \left(x^{\frac{13}{10}} + 3 y\right)}$$
With
$$n = 0$$
the equation
$$u = 0$$
its solution
$$u = 2 i n z \left(x^{\frac{13}{10}} + 3 y\right)$$
Коэффициент при z равен
$$- 2 i n \left(x^{\frac{13}{10}} + 3 y\right)$$
then possible cases for n :
$$n < 0$$
$$n = 0$$
Consider all cases in more detail:
With
$$n < 0$$
the equation
$$u + 2 i z \left(x^{\frac{13}{10}} + 3 y\right) = 0$$
its solution
$$z = \frac{i u}{2 \left(x^{\frac{13}{10}} + 3 y\right)}$$
With
$$n = 0$$
the equation
$$u = 0$$
its solution
The graph
Rapid solution
[src]
/ u \ / u \
im|-------------| I*re|-------------|
| / 13 \| | / 13 \|
| | -- || | | -- ||
| | 10 || | | 10 ||
\n*\x + 3*y// \n*\x + 3*y//
z1 = ----------------- - -------------------
2 2
$$z_{1} = - \frac{i \operatorname{re}{\left(\frac{u}{n \left(x^{\frac{13}{10}} + 3 y\right)}\right)}}{2} + \frac{\operatorname{im}{\left(\frac{u}{n \left(x^{\frac{13}{10}} + 3 y\right)}\right)}}{2}$$
z1 = -i*re(u/(n*(x^(13/10) + 3*y)))/2 + im(u/(n*(x^(13/10) + 3*y)))/2
Sum and product of roots
[src]
sum
/ u \ / u \
im|-------------| I*re|-------------|
| / 13 \| | / 13 \|
| | -- || | | -- ||
| | 10 || | | 10 ||
\n*\x + 3*y// \n*\x + 3*y//
----------------- - -------------------
2 2
$$- \frac{i \operatorname{re}{\left(\frac{u}{n \left(x^{\frac{13}{10}} + 3 y\right)}\right)}}{2} + \frac{\operatorname{im}{\left(\frac{u}{n \left(x^{\frac{13}{10}} + 3 y\right)}\right)}}{2}$$
=
/ u \ / u \
im|-------------| I*re|-------------|
| / 13 \| | / 13 \|
| | -- || | | -- ||
| | 10 || | | 10 ||
\n*\x + 3*y// \n*\x + 3*y//
----------------- - -------------------
2 2
$$- \frac{i \operatorname{re}{\left(\frac{u}{n \left(x^{\frac{13}{10}} + 3 y\right)}\right)}}{2} + \frac{\operatorname{im}{\left(\frac{u}{n \left(x^{\frac{13}{10}} + 3 y\right)}\right)}}{2}$$
product
/ u \ / u \
im|-------------| I*re|-------------|
| / 13 \| | / 13 \|
| | -- || | | -- ||
| | 10 || | | 10 ||
\n*\x + 3*y// \n*\x + 3*y//
----------------- - -------------------
2 2
$$- \frac{i \operatorname{re}{\left(\frac{u}{n \left(x^{\frac{13}{10}} + 3 y\right)}\right)}}{2} + \frac{\operatorname{im}{\left(\frac{u}{n \left(x^{\frac{13}{10}} + 3 y\right)}\right)}}{2}$$
=
/ u \ / u \
im|-------------| I*re|-------------|
| / 13 \| | / 13 \|
| | -- || | | -- ||
| | 10 || | | 10 ||
\n*\x + 3*y// \n*\x + 3*y//
----------------- - -------------------
2 2
$$- \frac{i \operatorname{re}{\left(\frac{u}{n \left(x^{\frac{13}{10}} + 3 y\right)}\right)}}{2} + \frac{\operatorname{im}{\left(\frac{u}{n \left(x^{\frac{13}{10}} + 3 y\right)}\right)}}{2}$$
im(u/(n*(x^(13/10) + 3*y)))/2 - i*re(u/(n*(x^(13/10) + 3*y)))/2