Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation (25+x)-10=40
-
Equation x^3+5*x^2-4*x-20=0
-
Equation x^2+4*x=21
-
Equation x^3+x-1=0
- Express {x} in terms of y where:
- 13*x+3*y=6
- -9*x+1*y=20
- 7*x-18*y=-4
- 5*x-13*y=-1
- Sum of series:
-
91
-
Identical expressions
- x(x- two)(three +x)= ninety-one
- x(x minus 2)(3 plus x) equally 91
- x(x minus two)(three plus x) equally ninety minus one
- xx-23+x=91
-
Similar expressions
- x(x+2)(3+x)=91
- 2(10x−16)2−9(10x−16)+4=0
- (1-1/25)(1-1/36)(1-1/49)(1-1/64)(1-1/81)(1-1/100)(1-1/121)(1-1/144)(1-1/169)(1-1/196)(x-1)=3/72*x^2+6*x+9=0
- 8/9(1/2v–18)+2v=2/3v
- x(x-2)(3-x)=91
- 175(x+6.9*10^-4)=1.3+x*175
x(x-2)(3+x)=91 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Rapid solution
[src]
___________________ / ___________________ \
/ ________ | / ________ |
/ 2401 \/ 637485 | ___ / 2401 \/ 637485 |
3 / ---- + ---------- | \/ 3 *3 / ---- + ---------- ___ |
1 19 \/ 54 18 | \/ 54 18 19*\/ 3 |
x1 = - - - --------------------------- - ------------------------ + I*|- ------------------------------ + ---------------------------|
3 ___________________ 2 | 2 ___________________|
/ ________ | / ________ |
/ 2401 \/ 637485 | / 2401 \/ 637485 |
18*3 / ---- + ---------- | 18*3 / ---- + ---------- |
\/ 54 18 \ \/ 54 18 /
$$x_{1} = - \frac{\sqrt[3]{\frac{\sqrt{637485}}{18} + \frac{2401}{54}}}{2} - \frac{1}{3} - \frac{19}{18 \sqrt[3]{\frac{\sqrt{637485}}{18} + \frac{2401}{54}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{637485}}{18} + \frac{2401}{54}}}{2} + \frac{19 \sqrt{3}}{18 \sqrt[3]{\frac{\sqrt{637485}}{18} + \frac{2401}{54}}}\right)$$
___________________ / ___________________ \
/ ________ | / ________ |
/ 2401 \/ 637485 | ___ / 2401 \/ 637485 |
3 / ---- + ---------- |\/ 3 *3 / ---- + ---------- ___ |
1 19 \/ 54 18 | \/ 54 18 19*\/ 3 |
x2 = - - - --------------------------- - ------------------------ + I*|------------------------------ - ---------------------------|
3 ___________________ 2 | 2 ___________________|
/ ________ | / ________ |
/ 2401 \/ 637485 | / 2401 \/ 637485 |
18*3 / ---- + ---------- | 18*3 / ---- + ---------- |
\/ 54 18 \ \/ 54 18 /
$$x_{2} = - \frac{\sqrt[3]{\frac{\sqrt{637485}}{18} + \frac{2401}{54}}}{2} - \frac{1}{3} - \frac{19}{18 \sqrt[3]{\frac{\sqrt{637485}}{18} + \frac{2401}{54}}} + i \left(- \frac{19 \sqrt{3}}{18 \sqrt[3]{\frac{\sqrt{637485}}{18} + \frac{2401}{54}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{637485}}{18} + \frac{2401}{54}}}{2}\right)$$
___________________
/ ________
1 / 2401 \/ 637485 19
x3 = - - + 3 / ---- + ---------- + --------------------------
3 \/ 54 18 ___________________
/ ________
/ 2401 \/ 637485
9*3 / ---- + ----------
\/ 54 18
$$x_{3} = - \frac{1}{3} + \frac{19}{9 \sqrt[3]{\frac{\sqrt{637485}}{18} + \frac{2401}{54}}} + \sqrt[3]{\frac{\sqrt{637485}}{18} + \frac{2401}{54}}$$
x3 = -1/3 + 19/(9*(sqrt(637485)/18 + 2401/54)^(1/3)) + (sqrt(637485)/18 + 2401/54)^(1/3)
Sum and product of roots
[src]
sum
___________________ / ___________________ \ ___________________ / ___________________ \
/ ________ | / ________ | / ________ | / ________ |
/ 2401 \/ 637485 | ___ / 2401 \/ 637485 | / 2401 \/ 637485 | ___ / 2401 \/ 637485 | ___________________
3 / ---- + ---------- | \/ 3 *3 / ---- + ---------- ___ | 3 / ---- + ---------- |\/ 3 *3 / ---- + ---------- ___ | / ________
1 19 \/ 54 18 | \/ 54 18 19*\/ 3 | 1 19 \/ 54 18 | \/ 54 18 19*\/ 3 | 1 / 2401 \/ 637485 19
- - - --------------------------- - ------------------------ + I*|- ------------------------------ + ---------------------------| + - - - --------------------------- - ------------------------ + I*|------------------------------ - ---------------------------| + - - + 3 / ---- + ---------- + --------------------------
3 ___________________ 2 | 2 ___________________| 3 ___________________ 2 | 2 ___________________| 3 \/ 54 18 ___________________
/ ________ | / ________ | / ________ | / ________ | / ________
/ 2401 \/ 637485 | / 2401 \/ 637485 | / 2401 \/ 637485 | / 2401 \/ 637485 | / 2401 \/ 637485
18*3 / ---- + ---------- | 18*3 / ---- + ---------- | 18*3 / ---- + ---------- | 18*3 / ---- + ---------- | 9*3 / ---- + ----------
\/ 54 18 \ \/ 54 18 / \/ 54 18 \ \/ 54 18 / \/ 54 18
$$\left(- \frac{1}{3} + \frac{19}{9 \sqrt[3]{\frac{\sqrt{637485}}{18} + \frac{2401}{54}}} + \sqrt[3]{\frac{\sqrt{637485}}{18} + \frac{2401}{54}}\right) + \left(\left(- \frac{\sqrt[3]{\frac{\sqrt{637485}}{18} + \frac{2401}{54}}}{2} - \frac{1}{3} - \frac{19}{18 \sqrt[3]{\frac{\sqrt{637485}}{18} + \frac{2401}{54}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{637485}}{18} + \frac{2401}{54}}}{2} + \frac{19 \sqrt{3}}{18 \sqrt[3]{\frac{\sqrt{637485}}{18} + \frac{2401}{54}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{\sqrt{637485}}{18} + \frac{2401}{54}}}{2} - \frac{1}{3} - \frac{19}{18 \sqrt[3]{\frac{\sqrt{637485}}{18} + \frac{2401}{54}}} + i \left(- \frac{19 \sqrt{3}}{18 \sqrt[3]{\frac{\sqrt{637485}}{18} + \frac{2401}{54}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{637485}}{18} + \frac{2401}{54}}}{2}\right)\right)\right)$$
=
/ ___________________ \ / ___________________ \
| / ________ | | / ________ |
| ___ / 2401 \/ 637485 | | ___ / 2401 \/ 637485 |
|\/ 3 *3 / ---- + ---------- ___ | | \/ 3 *3 / ---- + ---------- ___ |
| \/ 54 18 19*\/ 3 | | \/ 54 18 19*\/ 3 |
-1 + I*|------------------------------ - ---------------------------| + I*|- ------------------------------ + ---------------------------|
| 2 ___________________| | 2 ___________________|
| / ________ | | / ________ |
| / 2401 \/ 637485 | | / 2401 \/ 637485 |
| 18*3 / ---- + ---------- | | 18*3 / ---- + ---------- |
\ \/ 54 18 / \ \/ 54 18 /
$$-1 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{637485}}{18} + \frac{2401}{54}}}{2} + \frac{19 \sqrt{3}}{18 \sqrt[3]{\frac{\sqrt{637485}}{18} + \frac{2401}{54}}}\right) + i \left(- \frac{19 \sqrt{3}}{18 \sqrt[3]{\frac{\sqrt{637485}}{18} + \frac{2401}{54}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{637485}}{18} + \frac{2401}{54}}}{2}\right)$$
product
/ ___________________ / ___________________ \\ / ___________________ / ___________________ \\ | / ________ | / ________ || | / ________ | / ________ || | / 2401 \/ 637485 | ___ / 2401 \/ 637485 || | / 2401 \/ 637485 | ___ / 2401 \/ 637485 || / ___________________ \ | 3 / ---- + ---------- | \/ 3 *3 / ---- + ---------- ___ || | 3 / ---- + ---------- |\/ 3 *3 / ---- + ---------- ___ || | / ________ | | 1 19 \/ 54 18 | \/ 54 18 19*\/ 3 || | 1 19 \/ 54 18 | \/ 54 18 19*\/ 3 || | 1 / 2401 \/ 637485 19 | |- - - --------------------------- - ------------------------ + I*|- ------------------------------ + ---------------------------||*|- - - --------------------------- - ------------------------ + I*|------------------------------ - ---------------------------||*|- - + 3 / ---- + ---------- + --------------------------| | 3 ___________________ 2 | 2 ___________________|| | 3 ___________________ 2 | 2 ___________________|| | 3 \/ 54 18 ___________________| | / ________ | / ________ || | / ________ | / ________ || | / ________ | | / 2401 \/ 637485 | / 2401 \/ 637485 || | / 2401 \/ 637485 | / 2401 \/ 637485 || | / 2401 \/ 637485 | | 18*3 / ---- + ---------- | 18*3 / ---- + ---------- || | 18*3 / ---- + ---------- | 18*3 / ---- + ---------- || | 9*3 / ---- + ---------- | \ \/ 54 18 \ \/ 54 18 // \ \/ 54 18 \ \/ 54 18 // \ \/ 54 18 /
$$\left(- \frac{\sqrt[3]{\frac{\sqrt{637485}}{18} + \frac{2401}{54}}}{2} - \frac{1}{3} - \frac{19}{18 \sqrt[3]{\frac{\sqrt{637485}}{18} + \frac{2401}{54}}} + i \left(- \frac{19 \sqrt{3}}{18 \sqrt[3]{\frac{\sqrt{637485}}{18} + \frac{2401}{54}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{637485}}{18} + \frac{2401}{54}}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{\sqrt{637485}}{18} + \frac{2401}{54}}}{2} - \frac{1}{3} - \frac{19}{18 \sqrt[3]{\frac{\sqrt{637485}}{18} + \frac{2401}{54}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{637485}}{18} + \frac{2401}{54}}}{2} + \frac{19 \sqrt{3}}{18 \sqrt[3]{\frac{\sqrt{637485}}{18} + \frac{2401}{54}}}\right)\right) \left(- \frac{1}{3} + \frac{19}{9 \sqrt[3]{\frac{\sqrt{637485}}{18} + \frac{2401}{54}}} + \sqrt[3]{\frac{\sqrt{637485}}{18} + \frac{2401}{54}}\right)$$
=
91
$$91$$
91
Numerical answer
[src]
x1 = 4.60155914844392
x2 = -2.80077957422196 + 3.4542060624249*i
x3 = -2.80077957422196 - 3.4542060624249*i
x3 = -2.80077957422196 - 3.4542060624249*i