Mister Exam
Other calculators
-
How to use it?
- Equation:
- Equation z^3=-i
-
Equation 3*x^2+x-10=0
-
Equation 2x=5
-
Equation sin(x)=(-1)/sqrt(2)
- Express {x} in terms of y where:
- -8*x+14*y=5
- 17*x+7*y=-6
- -11*x-14*y=6
- -18*x-8*y=-5
- Sum of series:
-
(x-7)^3
-
Identical expressions
- (x- seven)^ three = nine (x+ seven)
- (x minus 7) cubed equally 9(x plus 7)
- (x minus seven) to the power of three equally nine (x plus seven)
- (x-7)3=9(x+7)
- x-73=9x+7
- (x-7)³=9(x+7)
- (x-7) to the power of 3=9(x+7)
- x-7^3=9x+7
-
Similar expressions
- (x+7)^3=49*(x+7)
- (x^2+9*x+7)/((x-5)^2*(x+1)^2)=-(3/((x-5)*(x+1)))
- (x+7)^3=9(x+7)
- (x-7)^3=9(x-7)
- -0,9x+71=8
(x-7)^3=9(x+7) equation
The teacher will be very surprised to see your correct solution 😉
The solution
Rapid solution
[src]
________________ / ________________ \
3 / _____ | ___ 3 / _____ ___ |
3 \/ 63 + 3*\/ 438 | \/ 3 *\/ 63 + 3*\/ 438 3*\/ 3 |
x1 = 7 - --------------------- - ------------------- + I*|- ------------------------- + ---------------------|
________________ 2 | 2 ________________|
3 / _____ | 3 / _____ |
2*\/ 63 + 3*\/ 438 \ 2*\/ 63 + 3*\/ 438 /
$$x_{1} = - \frac{\sqrt[3]{3 \sqrt{438} + 63}}{2} - \frac{3}{2 \sqrt[3]{3 \sqrt{438} + 63}} + 7 + i \left(- \frac{\sqrt{3} \sqrt[3]{3 \sqrt{438} + 63}}{2} + \frac{3 \sqrt{3}}{2 \sqrt[3]{3 \sqrt{438} + 63}}\right)$$
________________ / ________________ \
3 / _____ | ___ 3 / _____ ___ |
3 \/ 63 + 3*\/ 438 |\/ 3 *\/ 63 + 3*\/ 438 3*\/ 3 |
x2 = 7 - --------------------- - ------------------- + I*|------------------------- - ---------------------|
________________ 2 | 2 ________________|
3 / _____ | 3 / _____ |
2*\/ 63 + 3*\/ 438 \ 2*\/ 63 + 3*\/ 438 /
$$x_{2} = - \frac{\sqrt[3]{3 \sqrt{438} + 63}}{2} - \frac{3}{2 \sqrt[3]{3 \sqrt{438} + 63}} + 7 + i \left(- \frac{3 \sqrt{3}}{2 \sqrt[3]{3 \sqrt{438} + 63}} + \frac{\sqrt{3} \sqrt[3]{3 \sqrt{438} + 63}}{2}\right)$$
________________
3 / _____ 3
x3 = 7 + \/ 63 + 3*\/ 438 + -------------------
________________
3 / _____
\/ 63 + 3*\/ 438
$$x_{3} = \frac{3}{\sqrt[3]{3 \sqrt{438} + 63}} + \sqrt[3]{3 \sqrt{438} + 63} + 7$$
x3 = 3/(3*sqrt(438) + 63)^(1/3) + (3*sqrt(438) + 63)^(1/3) + 7
Sum and product of roots
[src]
sum
________________ / ________________ \ ________________ / ________________ \
3 / _____ | ___ 3 / _____ ___ | 3 / _____ | ___ 3 / _____ ___ | ________________
3 \/ 63 + 3*\/ 438 | \/ 3 *\/ 63 + 3*\/ 438 3*\/ 3 | 3 \/ 63 + 3*\/ 438 |\/ 3 *\/ 63 + 3*\/ 438 3*\/ 3 | 3 / _____ 3
7 - --------------------- - ------------------- + I*|- ------------------------- + ---------------------| + 7 - --------------------- - ------------------- + I*|------------------------- - ---------------------| + 7 + \/ 63 + 3*\/ 438 + -------------------
________________ 2 | 2 ________________| ________________ 2 | 2 ________________| ________________
3 / _____ | 3 / _____ | 3 / _____ | 3 / _____ | 3 / _____
2*\/ 63 + 3*\/ 438 \ 2*\/ 63 + 3*\/ 438 / 2*\/ 63 + 3*\/ 438 \ 2*\/ 63 + 3*\/ 438 / \/ 63 + 3*\/ 438
$$\left(\frac{3}{\sqrt[3]{3 \sqrt{438} + 63}} + \sqrt[3]{3 \sqrt{438} + 63} + 7\right) + \left(\left(- \frac{\sqrt[3]{3 \sqrt{438} + 63}}{2} - \frac{3}{2 \sqrt[3]{3 \sqrt{438} + 63}} + 7 + i \left(- \frac{\sqrt{3} \sqrt[3]{3 \sqrt{438} + 63}}{2} + \frac{3 \sqrt{3}}{2 \sqrt[3]{3 \sqrt{438} + 63}}\right)\right) + \left(- \frac{\sqrt[3]{3 \sqrt{438} + 63}}{2} - \frac{3}{2 \sqrt[3]{3 \sqrt{438} + 63}} + 7 + i \left(- \frac{3 \sqrt{3}}{2 \sqrt[3]{3 \sqrt{438} + 63}} + \frac{\sqrt{3} \sqrt[3]{3 \sqrt{438} + 63}}{2}\right)\right)\right)$$
=
/ ________________ \ / ________________ \
| ___ 3 / _____ ___ | | ___ 3 / _____ ___ |
|\/ 3 *\/ 63 + 3*\/ 438 3*\/ 3 | | \/ 3 *\/ 63 + 3*\/ 438 3*\/ 3 |
21 + I*|------------------------- - ---------------------| + I*|- ------------------------- + ---------------------|
| 2 ________________| | 2 ________________|
| 3 / _____ | | 3 / _____ |
\ 2*\/ 63 + 3*\/ 438 / \ 2*\/ 63 + 3*\/ 438 /
$$21 + i \left(- \frac{\sqrt{3} \sqrt[3]{3 \sqrt{438} + 63}}{2} + \frac{3 \sqrt{3}}{2 \sqrt[3]{3 \sqrt{438} + 63}}\right) + i \left(- \frac{3 \sqrt{3}}{2 \sqrt[3]{3 \sqrt{438} + 63}} + \frac{\sqrt{3} \sqrt[3]{3 \sqrt{438} + 63}}{2}\right)$$
product
/ ________________ / ________________ \\ / ________________ / ________________ \\ | 3 / _____ | ___ 3 / _____ ___ || | 3 / _____ | ___ 3 / _____ ___ || / ________________ \ | 3 \/ 63 + 3*\/ 438 | \/ 3 *\/ 63 + 3*\/ 438 3*\/ 3 || | 3 \/ 63 + 3*\/ 438 |\/ 3 *\/ 63 + 3*\/ 438 3*\/ 3 || | 3 / _____ 3 | |7 - --------------------- - ------------------- + I*|- ------------------------- + ---------------------||*|7 - --------------------- - ------------------- + I*|------------------------- - ---------------------||*|7 + \/ 63 + 3*\/ 438 + -------------------| | ________________ 2 | 2 ________________|| | ________________ 2 | 2 ________________|| | ________________| | 3 / _____ | 3 / _____ || | 3 / _____ | 3 / _____ || | 3 / _____ | \ 2*\/ 63 + 3*\/ 438 \ 2*\/ 63 + 3*\/ 438 // \ 2*\/ 63 + 3*\/ 438 \ 2*\/ 63 + 3*\/ 438 // \ \/ 63 + 3*\/ 438 /
$$\left(- \frac{\sqrt[3]{3 \sqrt{438} + 63}}{2} - \frac{3}{2 \sqrt[3]{3 \sqrt{438} + 63}} + 7 + i \left(- \frac{3 \sqrt{3}}{2 \sqrt[3]{3 \sqrt{438} + 63}} + \frac{\sqrt{3} \sqrt[3]{3 \sqrt{438} + 63}}{2}\right)\right) \left(- \frac{\sqrt[3]{3 \sqrt{438} + 63}}{2} - \frac{3}{2 \sqrt[3]{3 \sqrt{438} + 63}} + 7 + i \left(- \frac{\sqrt{3} \sqrt[3]{3 \sqrt{438} + 63}}{2} + \frac{3 \sqrt{3}}{2 \sqrt[3]{3 \sqrt{438} + 63}}\right)\right) \left(\frac{3}{\sqrt[3]{3 \sqrt{438} + 63}} + \sqrt[3]{3 \sqrt{438} + 63} + 7\right)$$
=
406
$$406$$
406
Numerical answer
[src]
x1 = 4.19540092945257 + 3.82064495073103*i
x2 = 12.6091981410949
x3 = 4.19540092945257 - 3.82064495073103*i
x3 = 4.19540092945257 - 3.82064495073103*i