Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation -x/12+x=55/12
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Equation 9/(x-2)=9/2
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Equation 2-3*(2*x+2)=5-4*x
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Equation -4x=15-3(3x-5)
- Express {x} in terms of y where:
- -10*x-18*y=15
- 2*x-15*y=-1
- -19*x-5*y=-16
- 13*x+7*y=11
- Integral of d{x}:
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2*x
- Limit of the function:
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2*x
- Derivative of:
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2*x
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Identical expressions
- √(x^ two - one)^ three = two *x
- √(x squared minus 1) cubed equally 2 multiply by x
- √(x to the power of two minus one) to the power of three equally two multiply by x
- √(x2-1)3=2*x
- √x2-13=2*x
- √(x²-1)³=2*x
- √(x to the power of 2-1) to the power of 3=2*x
- √(x^2-1)^3=2x
- √(x2-1)3=2x
- √x2-13=2x
- √x^2-1^3=2x
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Similar expressions
- 2x+2=-3
- x^2-2x+5=0
- √(x^2+1)^3=2*x
√(x^2-1)^3=2*x equation
The teacher will be very surprised to see your correct solution 😉
The solution
Sum and product of roots
[src]
sum
_____________ / _____________ \ _____________ / _____________ \
/ ____ | / ____ | / ____ | / ____ |
/ 19 \/ 33 | ___ / 19 \/ 33 | / 19 \/ 33 | ___ / 19 \/ 33 | _____________
3 / -- + ------ | \/ 3 *3 / -- + ------ ___ | 3 / -- + ------ |\/ 3 *3 / -- + ------ ___ | / ____
1 2 \/ 27 9 | \/ 27 9 2*\/ 3 | 1 2 \/ 27 9 | \/ 27 9 2*\/ 3 | 1 / 19 \/ 33 4
- - -------------------- - ------------------ + I*|- ------------------------ + --------------------| + - - -------------------- - ------------------ + I*|------------------------ - --------------------| + - + 3 / -- + ------ + --------------------
3 _____________ 2 | 2 _____________| 3 _____________ 2 | 2 _____________| 3 \/ 27 9 _____________
/ ____ | / ____ | / ____ | / ____ | / ____
/ 19 \/ 33 | / 19 \/ 33 | / 19 \/ 33 | / 19 \/ 33 | / 19 \/ 33
9*3 / -- + ------ | 9*3 / -- + ------ | 9*3 / -- + ------ | 9*3 / -- + ------ | 9*3 / -- + ------
\/ 27 9 \ \/ 27 9 / \/ 27 9 \ \/ 27 9 / \/ 27 9
$$\left(\frac{1}{3} + \frac{4}{9 \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}} + \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}\right) + \left(\left(- \frac{\sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}}{2} - \frac{2}{9 \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}} + \frac{1}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}}{2} + \frac{2 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}}{2} - \frac{2}{9 \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}} + \frac{1}{3} + i \left(- \frac{2 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}}{2}\right)\right)\right)$$
=
/ _____________ \ / _____________ \
| / ____ | | / ____ |
| ___ / 19 \/ 33 | | ___ / 19 \/ 33 |
|\/ 3 *3 / -- + ------ ___ | | \/ 3 *3 / -- + ------ ___ |
| \/ 27 9 2*\/ 3 | | \/ 27 9 2*\/ 3 |
1 + I*|------------------------ - --------------------| + I*|- ------------------------ + --------------------|
| 2 _____________| | 2 _____________|
| / ____ | | / ____ |
| / 19 \/ 33 | | / 19 \/ 33 |
| 9*3 / -- + ------ | | 9*3 / -- + ------ |
\ \/ 27 9 / \ \/ 27 9 /
$$1 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}}{2} + \frac{2 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}}\right) + i \left(- \frac{2 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}}{2}\right)$$
product
/ _____________ / _____________ \\ / _____________ / _____________ \\ | / ____ | / ____ || | / ____ | / ____ || | / 19 \/ 33 | ___ / 19 \/ 33 || | / 19 \/ 33 | ___ / 19 \/ 33 || / _____________ \ | 3 / -- + ------ | \/ 3 *3 / -- + ------ ___ || | 3 / -- + ------ |\/ 3 *3 / -- + ------ ___ || | / ____ | |1 2 \/ 27 9 | \/ 27 9 2*\/ 3 || |1 2 \/ 27 9 | \/ 27 9 2*\/ 3 || |1 / 19 \/ 33 4 | |- - -------------------- - ------------------ + I*|- ------------------------ + --------------------||*|- - -------------------- - ------------------ + I*|------------------------ - --------------------||*|- + 3 / -- + ------ + --------------------| |3 _____________ 2 | 2 _____________|| |3 _____________ 2 | 2 _____________|| |3 \/ 27 9 _____________| | / ____ | / ____ || | / ____ | / ____ || | / ____ | | / 19 \/ 33 | / 19 \/ 33 || | / 19 \/ 33 | / 19 \/ 33 || | / 19 \/ 33 | | 9*3 / -- + ------ | 9*3 / -- + ------ || | 9*3 / -- + ------ | 9*3 / -- + ------ || | 9*3 / -- + ------ | \ \/ 27 9 \ \/ 27 9 // \ \/ 27 9 \ \/ 27 9 // \ \/ 27 9 /
$$\left(- \frac{\sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}}{2} - \frac{2}{9 \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}} + \frac{1}{3} + i \left(- \frac{2 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}}{2} - \frac{2}{9 \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}} + \frac{1}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}}{2} + \frac{2 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}}\right)\right) \left(\frac{1}{3} + \frac{4}{9 \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}} + \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}\right)$$
=
1
$$1$$
1
Rapid solution
[src]
_____________ / _____________ \
/ ____ | / ____ |
/ 19 \/ 33 | ___ / 19 \/ 33 |
3 / -- + ------ | \/ 3 *3 / -- + ------ ___ |
1 2 \/ 27 9 | \/ 27 9 2*\/ 3 |
x1 = - - -------------------- - ------------------ + I*|- ------------------------ + --------------------|
3 _____________ 2 | 2 _____________|
/ ____ | / ____ |
/ 19 \/ 33 | / 19 \/ 33 |
9*3 / -- + ------ | 9*3 / -- + ------ |
\/ 27 9 \ \/ 27 9 /
$$x_{1} = - \frac{\sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}}{2} - \frac{2}{9 \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}} + \frac{1}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}}{2} + \frac{2 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}}\right)$$
_____________ / _____________ \
/ ____ | / ____ |
/ 19 \/ 33 | ___ / 19 \/ 33 |
3 / -- + ------ |\/ 3 *3 / -- + ------ ___ |
1 2 \/ 27 9 | \/ 27 9 2*\/ 3 |
x2 = - - -------------------- - ------------------ + I*|------------------------ - --------------------|
3 _____________ 2 | 2 _____________|
/ ____ | / ____ |
/ 19 \/ 33 | / 19 \/ 33 |
9*3 / -- + ------ | 9*3 / -- + ------ |
\/ 27 9 \ \/ 27 9 /
$$x_{2} = - \frac{\sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}}{2} - \frac{2}{9 \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}} + \frac{1}{3} + i \left(- \frac{2 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}}{2}\right)$$
_____________
/ ____
1 / 19 \/ 33 4
x3 = - + 3 / -- + ------ + --------------------
3 \/ 27 9 _____________
/ ____
/ 19 \/ 33
9*3 / -- + ------
\/ 27 9
$$x_{3} = \frac{1}{3} + \frac{4}{9 \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}} + \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}$$
x3 = 1/3 + 4/(9*(sqrt(33)/9 + 19/27)^(1/3)) + (sqrt(33)/9 + 19/27)^(1/3)
Numerical answer
[src]
x1 = -0.419643377607081 - 0.606290729207199*i
x2 = -0.419643377607081 + 0.606290729207199*i
x3 = 1.83928675521416
x3 = 1.83928675521416
The graph