Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^2=12
-
Equation 12-x^2=11
-
Equation -sin(x)=0
-
Equation 4x+5=2x-7
- Express {x} in terms of y where:
- -5*x-6*y=-1
- -17*x-15*y=-17
- -2*x+7*y=-14
- -11*x-1*y=15
-
Identical expressions
- (x+ three)(x+ four)(x+ five)= four thousand, seven hundred and thirty-five
- (x plus 3)(x plus 4)(x plus 5) equally 4735
- (x plus three)(x plus four)(x plus five) equally four thousand, seven hundred and thirty minus five
- x+3x+4x+5=4735
-
Similar expressions
- (x+3)(x-4)(x+5)=4735
- x+2x+3x+4x+5x+6x+7x=100
- x+2x+3x+4x+5x+6x+7x=365
- (x+3)(x+4)(x-5)=4735
- (x-3)(x+4)(x+5)=4735
(x+3)(x+4)(x+5)=4735 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
(x + 3)*(x + 4)*(x + 5) = 4735
$$\left(x + 3\right) \left(x + 4\right) \left(x + 5\right) = 4735$$
Rapid solution
[src]
_______________________ / _______________________ \
/ ____________ | / ____________ |
/ 4735 \/ 1816038213 | ___ / 4735 \/ 1816038213 |
3 / ---- + -------------- | \/ 3 *3 / ---- + -------------- ___ |
\/ 2 18 1 | \/ 2 18 \/ 3 |
x1 = -4 - ---------------------------- - ------------------------------ + I*|- ---------------------------------- + ------------------------------|
2 _______________________ | 2 _______________________|
/ ____________ | / ____________ |
/ 4735 \/ 1816038213 | / 4735 \/ 1816038213 |
6*3 / ---- + -------------- | 6*3 / ---- + -------------- |
\/ 2 18 \ \/ 2 18 /
$$x_{1} = - \frac{\sqrt[3]{\frac{\sqrt{1816038213}}{18} + \frac{4735}{2}}}{2} - 4 - \frac{1}{6 \sqrt[3]{\frac{\sqrt{1816038213}}{18} + \frac{4735}{2}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{1816038213}}{18} + \frac{4735}{2}}}{2} + \frac{\sqrt{3}}{6 \sqrt[3]{\frac{\sqrt{1816038213}}{18} + \frac{4735}{2}}}\right)$$
_______________________ / _______________________ \
/ ____________ | / ____________ |
/ 4735 \/ 1816038213 | ___ / 4735 \/ 1816038213 |
3 / ---- + -------------- |\/ 3 *3 / ---- + -------------- ___ |
\/ 2 18 1 | \/ 2 18 \/ 3 |
x2 = -4 - ---------------------------- - ------------------------------ + I*|---------------------------------- - ------------------------------|
2 _______________________ | 2 _______________________|
/ ____________ | / ____________ |
/ 4735 \/ 1816038213 | / 4735 \/ 1816038213 |
6*3 / ---- + -------------- | 6*3 / ---- + -------------- |
\/ 2 18 \ \/ 2 18 /
$$x_{2} = - \frac{\sqrt[3]{\frac{\sqrt{1816038213}}{18} + \frac{4735}{2}}}{2} - 4 - \frac{1}{6 \sqrt[3]{\frac{\sqrt{1816038213}}{18} + \frac{4735}{2}}} + i \left(- \frac{\sqrt{3}}{6 \sqrt[3]{\frac{\sqrt{1816038213}}{18} + \frac{4735}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{1816038213}}{18} + \frac{4735}{2}}}{2}\right)$$
_______________________
/ ____________
/ 4735 \/ 1816038213 1
x3 = -4 + 3 / ---- + -------------- + ------------------------------
\/ 2 18 _______________________
/ ____________
/ 4735 \/ 1816038213
3*3 / ---- + --------------
\/ 2 18
$$x_{3} = -4 + \frac{1}{3 \sqrt[3]{\frac{\sqrt{1816038213}}{18} + \frac{4735}{2}}} + \sqrt[3]{\frac{\sqrt{1816038213}}{18} + \frac{4735}{2}}$$
x3 = -4 + 1/(3*(sqrt(1816038213)/18 + 4735/2)^(1/3)) + (sqrt(1816038213)/18 + 4735/2)^(1/3)
Sum and product of roots
[src]
sum
_______________________ / _______________________ \ _______________________ / _______________________ \
/ ____________ | / ____________ | / ____________ | / ____________ |
/ 4735 \/ 1816038213 | ___ / 4735 \/ 1816038213 | / 4735 \/ 1816038213 | ___ / 4735 \/ 1816038213 | _______________________
3 / ---- + -------------- | \/ 3 *3 / ---- + -------------- ___ | 3 / ---- + -------------- |\/ 3 *3 / ---- + -------------- ___ | / ____________
\/ 2 18 1 | \/ 2 18 \/ 3 | \/ 2 18 1 | \/ 2 18 \/ 3 | / 4735 \/ 1816038213 1
-4 - ---------------------------- - ------------------------------ + I*|- ---------------------------------- + ------------------------------| + -4 - ---------------------------- - ------------------------------ + I*|---------------------------------- - ------------------------------| + -4 + 3 / ---- + -------------- + ------------------------------
2 _______________________ | 2 _______________________| 2 _______________________ | 2 _______________________| \/ 2 18 _______________________
/ ____________ | / ____________ | / ____________ | / ____________ | / ____________
/ 4735 \/ 1816038213 | / 4735 \/ 1816038213 | / 4735 \/ 1816038213 | / 4735 \/ 1816038213 | / 4735 \/ 1816038213
6*3 / ---- + -------------- | 6*3 / ---- + -------------- | 6*3 / ---- + -------------- | 6*3 / ---- + -------------- | 3*3 / ---- + --------------
\/ 2 18 \ \/ 2 18 / \/ 2 18 \ \/ 2 18 / \/ 2 18
$$\left(-4 + \frac{1}{3 \sqrt[3]{\frac{\sqrt{1816038213}}{18} + \frac{4735}{2}}} + \sqrt[3]{\frac{\sqrt{1816038213}}{18} + \frac{4735}{2}}\right) + \left(\left(- \frac{\sqrt[3]{\frac{\sqrt{1816038213}}{18} + \frac{4735}{2}}}{2} - 4 - \frac{1}{6 \sqrt[3]{\frac{\sqrt{1816038213}}{18} + \frac{4735}{2}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{1816038213}}{18} + \frac{4735}{2}}}{2} + \frac{\sqrt{3}}{6 \sqrt[3]{\frac{\sqrt{1816038213}}{18} + \frac{4735}{2}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{\sqrt{1816038213}}{18} + \frac{4735}{2}}}{2} - 4 - \frac{1}{6 \sqrt[3]{\frac{\sqrt{1816038213}}{18} + \frac{4735}{2}}} + i \left(- \frac{\sqrt{3}}{6 \sqrt[3]{\frac{\sqrt{1816038213}}{18} + \frac{4735}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{1816038213}}{18} + \frac{4735}{2}}}{2}\right)\right)\right)$$
=
/ _______________________ \ / _______________________ \
| / ____________ | | / ____________ |
| ___ / 4735 \/ 1816038213 | | ___ / 4735 \/ 1816038213 |
|\/ 3 *3 / ---- + -------------- ___ | | \/ 3 *3 / ---- + -------------- ___ |
| \/ 2 18 \/ 3 | | \/ 2 18 \/ 3 |
-12 + I*|---------------------------------- - ------------------------------| + I*|- ---------------------------------- + ------------------------------|
| 2 _______________________| | 2 _______________________|
| / ____________ | | / ____________ |
| / 4735 \/ 1816038213 | | / 4735 \/ 1816038213 |
| 6*3 / ---- + -------------- | | 6*3 / ---- + -------------- |
\ \/ 2 18 / \ \/ 2 18 /
$$-12 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{1816038213}}{18} + \frac{4735}{2}}}{2} + \frac{\sqrt{3}}{6 \sqrt[3]{\frac{\sqrt{1816038213}}{18} + \frac{4735}{2}}}\right) + i \left(- \frac{\sqrt{3}}{6 \sqrt[3]{\frac{\sqrt{1816038213}}{18} + \frac{4735}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{1816038213}}{18} + \frac{4735}{2}}}{2}\right)$$
product
/ _______________________ / _______________________ \\ / _______________________ / _______________________ \\ | / ____________ | / ____________ || | / ____________ | / ____________ || | / 4735 \/ 1816038213 | ___ / 4735 \/ 1816038213 || | / 4735 \/ 1816038213 | ___ / 4735 \/ 1816038213 || / _______________________ \ | 3 / ---- + -------------- | \/ 3 *3 / ---- + -------------- ___ || | 3 / ---- + -------------- |\/ 3 *3 / ---- + -------------- ___ || | / ____________ | | \/ 2 18 1 | \/ 2 18 \/ 3 || | \/ 2 18 1 | \/ 2 18 \/ 3 || | / 4735 \/ 1816038213 1 | |-4 - ---------------------------- - ------------------------------ + I*|- ---------------------------------- + ------------------------------||*|-4 - ---------------------------- - ------------------------------ + I*|---------------------------------- - ------------------------------||*|-4 + 3 / ---- + -------------- + ------------------------------| | 2 _______________________ | 2 _______________________|| | 2 _______________________ | 2 _______________________|| | \/ 2 18 _______________________| | / ____________ | / ____________ || | / ____________ | / ____________ || | / ____________ | | / 4735 \/ 1816038213 | / 4735 \/ 1816038213 || | / 4735 \/ 1816038213 | / 4735 \/ 1816038213 || | / 4735 \/ 1816038213 | | 6*3 / ---- + -------------- | 6*3 / ---- + -------------- || | 6*3 / ---- + -------------- | 6*3 / ---- + -------------- || | 3*3 / ---- + -------------- | \ \/ 2 18 \ \/ 2 18 // \ \/ 2 18 \ \/ 2 18 // \ \/ 2 18 /
$$\left(- \frac{\sqrt[3]{\frac{\sqrt{1816038213}}{18} + \frac{4735}{2}}}{2} - 4 - \frac{1}{6 \sqrt[3]{\frac{\sqrt{1816038213}}{18} + \frac{4735}{2}}} + i \left(- \frac{\sqrt{3}}{6 \sqrt[3]{\frac{\sqrt{1816038213}}{18} + \frac{4735}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{1816038213}}{18} + \frac{4735}{2}}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{\sqrt{1816038213}}{18} + \frac{4735}{2}}}{2} - 4 - \frac{1}{6 \sqrt[3]{\frac{\sqrt{1816038213}}{18} + \frac{4735}{2}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{1816038213}}{18} + \frac{4735}{2}}}{2} + \frac{\sqrt{3}}{6 \sqrt[3]{\frac{\sqrt{1816038213}}{18} + \frac{4735}{2}}}\right)\right) \left(-4 + \frac{1}{3 \sqrt[3]{\frac{\sqrt{1816038213}}{18} + \frac{4735}{2}}} + \sqrt[3]{\frac{\sqrt{1816038213}}{18} + \frac{4735}{2}}\right)$$
=
____________________________ 2/3 ___________________________ ____________________________ 2/3 ___________________________ 2/3 2/3
3 / ____________ 3 ___ / ____________\ 2/3 3 / ____________ ____________ 3 / ____________ 3 ____ / ____________\ 2/3 ____________ 3 / ____________ 3 ___ ____________ / ____________\ 3 ___ 6 ___ ___________ / ____________\
14205*\/ 511380 + 12*\/ 1816038213 201782025*\/ 2 *\127845 + 3*\/ 1816038213 / 14205*2 *\/ 127845 + 3*\/ 1816038213 \/ 1816038213 *\/ 511380 + 12*\/ 1816038213 201782025*\/ 18 *\42615 + \/ 1816038213 / 2 *\/ 1816038213 *\/ 127845 + 3*\/ 1816038213 4735*\/ 2 *\/ 1816038213 *\127845 + 3*\/ 1816038213 / 14205*\/ 2 *\/ 3 *\/ 605346071 *\42615 + \/ 1816038213 /
4675 + ------------------------------------- - ---------------------------------------------- - ----------------------------------------- - ---------------------------------------------- + -------------------------------------------- + -------------------------------------------------- + -------------------------------------------------------- - -----------------------------------------------------------
4 8 4 12 8 12 8 8
$$- \frac{201782025 \sqrt[3]{2} \left(3 \sqrt{1816038213} + 127845\right)^{\frac{2}{3}}}{8} - \frac{14205 \sqrt[3]{2} \sqrt[6]{3} \sqrt{605346071} \left(\sqrt{1816038213} + 42615\right)^{\frac{2}{3}}}{8} - \frac{14205 \cdot 2^{\frac{2}{3}} \sqrt[3]{3 \sqrt{1816038213} + 127845}}{4} - \frac{\sqrt{1816038213} \sqrt[3]{12 \sqrt{1816038213} + 511380}}{12} + 4675 + \frac{\sqrt{1816038213} \cdot 2^{\frac{2}{3}} \sqrt[3]{3 \sqrt{1816038213} + 127845}}{12} + \frac{14205 \sqrt[3]{12 \sqrt{1816038213} + 511380}}{4} + \frac{4735 \sqrt{1816038213} \sqrt[3]{2} \left(3 \sqrt{1816038213} + 127845\right)^{\frac{2}{3}}}{8} + \frac{201782025 \sqrt[3]{18} \left(\sqrt{1816038213} + 42615\right)^{\frac{2}{3}}}{8}$$
4675 + 14205*(511380 + 12*sqrt(1816038213))^(1/3)/4 - 201782025*2^(1/3)*(127845 + 3*sqrt(1816038213))^(2/3)/8 - 14205*2^(2/3)*(127845 + 3*sqrt(1816038213))^(1/3)/4 - sqrt(1816038213)*(511380 + 12*sqrt(1816038213))^(1/3)/12 + 201782025*18^(1/3)*(42615 + sqrt(1816038213))^(2/3)/8 + 2^(2/3)*sqrt(1816038213)*(127845 + 3*sqrt(1816038213))^(1/3)/12 + 4735*2^(1/3)*sqrt(1816038213)*(127845 + 3*sqrt(1816038213))^(2/3)/8 - 14205*2^(1/3)*3^(1/6)*sqrt(605346071)*(42615 + sqrt(1816038213))^(2/3)/8
Numerical answer
[src]
x1 = 12.8120142876758
x2 = -12.4060071438379 + 14.5252493371632*i
x3 = -12.4060071438379 - 14.5252493371632*i
x3 = -12.4060071438379 - 14.5252493371632*i