Mister Exam
Other calculators
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How to use it?
- Equation:
- Equation 64-x^2=0
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Equation 2*x^2+7*x-4=0
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Equation 11/(x+4)=-11/7
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Equation x^6=(x-5)^3
- Express {x} in terms of y where:
- 10*x-6*y=10
- 20*x+6*y=7
- 17*x-7*y=7
- 3*x+9*y=7
- Graphing y =:
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x^6
- Integral of d{x}:
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x^6
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(x-5)^3
- Derivative of:
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x^6
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(x-5)^3
- Canonical form:
- (x-5)^3
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Identical expressions
- x^ six =(x- five)^ three
- x to the power of 6 equally (x minus 5) cubed
- x to the power of six equally (x minus five) to the power of three
- x6=(x-5)3
- x6=x-53
- x⁶=(x-5)³
- x to the power of 6=(x-5) to the power of 3
- x^6=x-5^3
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Similar expressions
- x^6=(x+5)^3
x^6=(x-5)^3 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Rapid solution
[src]
/ / / ___\\\ / / ___\\
| | |21*\/ 3 ||| | |21*\/ 3 ||
| |atan|--------||| |atan|--------||
| 4 _____ | \ 19 /|| 4 _____ | \ 19 /|
| ___ \/ 421 *sin|--------------|| \/ 421 *cos|--------------|
1 | \/ 3 \ 2 /| \ 2 /
x1 = - - + I*|- ----- + ---------------------------| + ---------------------------
4 \ 4 2 / 2
$$x_{1} = - \frac{1}{4} + \frac{\sqrt[4]{421} \cos{\left(\frac{\operatorname{atan}{\left(\frac{21 \sqrt{3}}{19} \right)}}{2} \right)}}{2} + i \left(- \frac{\sqrt{3}}{4} + \frac{\sqrt[4]{421} \sin{\left(\frac{\operatorname{atan}{\left(\frac{21 \sqrt{3}}{19} \right)}}{2} \right)}}{2}\right)$$
/ / / ___\\\ / / ___\\
| | |21*\/ 3 ||| | |21*\/ 3 ||
| |atan|--------||| |atan|--------||
| 4 _____ | \ 19 /|| 4 _____ | \ 19 /|
| ___ \/ 421 *sin|--------------|| \/ 421 *cos|--------------|
1 |\/ 3 \ 2 /| \ 2 /
x2 = - - + I*|----- + ---------------------------| - ---------------------------
4 \ 4 2 / 2
$$x_{2} = - \frac{\sqrt[4]{421} \cos{\left(\frac{\operatorname{atan}{\left(\frac{21 \sqrt{3}}{19} \right)}}{2} \right)}}{2} - \frac{1}{4} + i \left(\frac{\sqrt{3}}{4} + \frac{\sqrt[4]{421} \sin{\left(\frac{\operatorname{atan}{\left(\frac{21 \sqrt{3}}{19} \right)}}{2} \right)}}{2}\right)$$
/ / / ___\\\ / / ___\\
| | |21*\/ 3 ||| | |21*\/ 3 ||
| |atan|--------||| |atan|--------||
| 4 _____ | \ 19 /|| 4 _____ | \ 19 /|
| ___ \/ 421 *sin|--------------|| \/ 421 *cos|--------------|
1 |\/ 3 \ 2 /| \ 2 /
x3 = - - + I*|----- - ---------------------------| + ---------------------------
4 \ 4 2 / 2
$$x_{3} = - \frac{1}{4} + \frac{\sqrt[4]{421} \cos{\left(\frac{\operatorname{atan}{\left(\frac{21 \sqrt{3}}{19} \right)}}{2} \right)}}{2} + i \left(- \frac{\sqrt[4]{421} \sin{\left(\frac{\operatorname{atan}{\left(\frac{21 \sqrt{3}}{19} \right)}}{2} \right)}}{2} + \frac{\sqrt{3}}{4}\right)$$
/ / / ___\\\ / / ___\\
| | |21*\/ 3 ||| | |21*\/ 3 ||
| |atan|--------||| |atan|--------||
| 4 _____ | \ 19 /|| 4 _____ | \ 19 /|
| ___ \/ 421 *sin|--------------|| \/ 421 *cos|--------------|
1 | \/ 3 \ 2 /| \ 2 /
x4 = - - + I*|- ----- - ---------------------------| - ---------------------------
4 \ 4 2 / 2
$$x_{4} = - \frac{\sqrt[4]{421} \cos{\left(\frac{\operatorname{atan}{\left(\frac{21 \sqrt{3}}{19} \right)}}{2} \right)}}{2} - \frac{1}{4} + i \left(- \frac{\sqrt[4]{421} \sin{\left(\frac{\operatorname{atan}{\left(\frac{21 \sqrt{3}}{19} \right)}}{2} \right)}}{2} - \frac{\sqrt{3}}{4}\right)$$
____
1 I*\/ 19
x5 = - - --------
2 2
$$x_{5} = \frac{1}{2} - \frac{\sqrt{19} i}{2}$$
____
1 I*\/ 19
x6 = - + --------
2 2
$$x_{6} = \frac{1}{2} + \frac{\sqrt{19} i}{2}$$
x6 = 1/2 + sqrt(19)*i/2
Sum and product of roots
[src]
sum
/ / / ___\\\ / / ___\\ / / / ___\\\ / / ___\\ / / / ___\\\ / / ___\\ / / / ___\\\ / / ___\\
| | |21*\/ 3 ||| | |21*\/ 3 || | | |21*\/ 3 ||| | |21*\/ 3 || | | |21*\/ 3 ||| | |21*\/ 3 || | | |21*\/ 3 ||| | |21*\/ 3 ||
| |atan|--------||| |atan|--------|| | |atan|--------||| |atan|--------|| | |atan|--------||| |atan|--------|| | |atan|--------||| |atan|--------||
| 4 _____ | \ 19 /|| 4 _____ | \ 19 /| | 4 _____ | \ 19 /|| 4 _____ | \ 19 /| | 4 _____ | \ 19 /|| 4 _____ | \ 19 /| | 4 _____ | \ 19 /|| 4 _____ | \ 19 /|
| ___ \/ 421 *sin|--------------|| \/ 421 *cos|--------------| | ___ \/ 421 *sin|--------------|| \/ 421 *cos|--------------| | ___ \/ 421 *sin|--------------|| \/ 421 *cos|--------------| | ___ \/ 421 *sin|--------------|| \/ 421 *cos|--------------| ____ ____
1 | \/ 3 \ 2 /| \ 2 / 1 |\/ 3 \ 2 /| \ 2 / 1 |\/ 3 \ 2 /| \ 2 / 1 | \/ 3 \ 2 /| \ 2 / 1 I*\/ 19 1 I*\/ 19
- - + I*|- ----- + ---------------------------| + --------------------------- + - - + I*|----- + ---------------------------| - --------------------------- + - - + I*|----- - ---------------------------| + --------------------------- + - - + I*|- ----- - ---------------------------| - --------------------------- + - - -------- + - + --------
4 \ 4 2 / 2 4 \ 4 2 / 2 4 \ 4 2 / 2 4 \ 4 2 / 2 2 2 2 2
$$\left(\left(\frac{1}{2} - \frac{\sqrt{19} i}{2}\right) + \left(\left(- \frac{\sqrt[4]{421} \cos{\left(\frac{\operatorname{atan}{\left(\frac{21 \sqrt{3}}{19} \right)}}{2} \right)}}{2} - \frac{1}{4} + i \left(- \frac{\sqrt[4]{421} \sin{\left(\frac{\operatorname{atan}{\left(\frac{21 \sqrt{3}}{19} \right)}}{2} \right)}}{2} - \frac{\sqrt{3}}{4}\right)\right) + \left(\left(- \frac{1}{4} + \frac{\sqrt[4]{421} \cos{\left(\frac{\operatorname{atan}{\left(\frac{21 \sqrt{3}}{19} \right)}}{2} \right)}}{2} + i \left(- \frac{\sqrt[4]{421} \sin{\left(\frac{\operatorname{atan}{\left(\frac{21 \sqrt{3}}{19} \right)}}{2} \right)}}{2} + \frac{\sqrt{3}}{4}\right)\right) + \left(\left(- \frac{1}{4} + \frac{\sqrt[4]{421} \cos{\left(\frac{\operatorname{atan}{\left(\frac{21 \sqrt{3}}{19} \right)}}{2} \right)}}{2} + i \left(- \frac{\sqrt{3}}{4} + \frac{\sqrt[4]{421} \sin{\left(\frac{\operatorname{atan}{\left(\frac{21 \sqrt{3}}{19} \right)}}{2} \right)}}{2}\right)\right) + \left(- \frac{\sqrt[4]{421} \cos{\left(\frac{\operatorname{atan}{\left(\frac{21 \sqrt{3}}{19} \right)}}{2} \right)}}{2} - \frac{1}{4} + i \left(\frac{\sqrt{3}}{4} + \frac{\sqrt[4]{421} \sin{\left(\frac{\operatorname{atan}{\left(\frac{21 \sqrt{3}}{19} \right)}}{2} \right)}}{2}\right)\right)\right)\right)\right)\right) + \left(\frac{1}{2} + \frac{\sqrt{19} i}{2}\right)$$
=
/ / / ___\\\ / / / ___\\\ / / / ___\\\ / / / ___\\\ | | |21*\/ 3 ||| | | |21*\/ 3 ||| | | |21*\/ 3 ||| | | |21*\/ 3 ||| | |atan|--------||| | |atan|--------||| | |atan|--------||| | |atan|--------||| | 4 _____ | \ 19 /|| | 4 _____ | \ 19 /|| | 4 _____ | \ 19 /|| | 4 _____ | \ 19 /|| | ___ \/ 421 *sin|--------------|| | ___ \/ 421 *sin|--------------|| | ___ \/ 421 *sin|--------------|| | ___ \/ 421 *sin|--------------|| | \/ 3 \ 2 /| | \/ 3 \ 2 /| |\/ 3 \ 2 /| |\/ 3 \ 2 /| I*|- ----- + ---------------------------| + I*|- ----- - ---------------------------| + I*|----- + ---------------------------| + I*|----- - ---------------------------| \ 4 2 / \ 4 2 / \ 4 2 / \ 4 2 /
$$i \left(- \frac{\sqrt[4]{421} \sin{\left(\frac{\operatorname{atan}{\left(\frac{21 \sqrt{3}}{19} \right)}}{2} \right)}}{2} - \frac{\sqrt{3}}{4}\right) + i \left(- \frac{\sqrt[4]{421} \sin{\left(\frac{\operatorname{atan}{\left(\frac{21 \sqrt{3}}{19} \right)}}{2} \right)}}{2} + \frac{\sqrt{3}}{4}\right) + i \left(- \frac{\sqrt{3}}{4} + \frac{\sqrt[4]{421} \sin{\left(\frac{\operatorname{atan}{\left(\frac{21 \sqrt{3}}{19} \right)}}{2} \right)}}{2}\right) + i \left(\frac{\sqrt{3}}{4} + \frac{\sqrt[4]{421} \sin{\left(\frac{\operatorname{atan}{\left(\frac{21 \sqrt{3}}{19} \right)}}{2} \right)}}{2}\right)$$
product
/ / / / ___\\\ / / ___\\\ / / / / ___\\\ / / ___\\\ / / / / ___\\\ / / ___\\\ / / / / ___\\\ / / ___\\\ | | | |21*\/ 3 ||| | |21*\/ 3 ||| | | | |21*\/ 3 ||| | |21*\/ 3 ||| | | | |21*\/ 3 ||| | |21*\/ 3 ||| | | | |21*\/ 3 ||| | |21*\/ 3 ||| | | |atan|--------||| |atan|--------||| | | |atan|--------||| |atan|--------||| | | |atan|--------||| |atan|--------||| | | |atan|--------||| |atan|--------||| | | 4 _____ | \ 19 /|| 4 _____ | \ 19 /|| | | 4 _____ | \ 19 /|| 4 _____ | \ 19 /|| | | 4 _____ | \ 19 /|| 4 _____ | \ 19 /|| | | 4 _____ | \ 19 /|| 4 _____ | \ 19 /|| | | ___ \/ 421 *sin|--------------|| \/ 421 *cos|--------------|| | | ___ \/ 421 *sin|--------------|| \/ 421 *cos|--------------|| | | ___ \/ 421 *sin|--------------|| \/ 421 *cos|--------------|| | | ___ \/ 421 *sin|--------------|| \/ 421 *cos|--------------|| / ____\ / ____\ | 1 | \/ 3 \ 2 /| \ 2 /| | 1 |\/ 3 \ 2 /| \ 2 /| | 1 |\/ 3 \ 2 /| \ 2 /| | 1 | \/ 3 \ 2 /| \ 2 /| |1 I*\/ 19 | |1 I*\/ 19 | |- - + I*|- ----- + ---------------------------| + ---------------------------|*|- - + I*|----- + ---------------------------| - ---------------------------|*|- - + I*|----- - ---------------------------| + ---------------------------|*|- - + I*|- ----- - ---------------------------| - ---------------------------|*|- - --------|*|- + --------| \ 4 \ 4 2 / 2 / \ 4 \ 4 2 / 2 / \ 4 \ 4 2 / 2 / \ 4 \ 4 2 / 2 / \2 2 / \2 2 /
$$\left(- \frac{1}{4} + \frac{\sqrt[4]{421} \cos{\left(\frac{\operatorname{atan}{\left(\frac{21 \sqrt{3}}{19} \right)}}{2} \right)}}{2} + i \left(- \frac{\sqrt{3}}{4} + \frac{\sqrt[4]{421} \sin{\left(\frac{\operatorname{atan}{\left(\frac{21 \sqrt{3}}{19} \right)}}{2} \right)}}{2}\right)\right) \left(- \frac{\sqrt[4]{421} \cos{\left(\frac{\operatorname{atan}{\left(\frac{21 \sqrt{3}}{19} \right)}}{2} \right)}}{2} - \frac{1}{4} + i \left(\frac{\sqrt{3}}{4} + \frac{\sqrt[4]{421} \sin{\left(\frac{\operatorname{atan}{\left(\frac{21 \sqrt{3}}{19} \right)}}{2} \right)}}{2}\right)\right) \left(- \frac{1}{4} + \frac{\sqrt[4]{421} \cos{\left(\frac{\operatorname{atan}{\left(\frac{21 \sqrt{3}}{19} \right)}}{2} \right)}}{2} + i \left(- \frac{\sqrt[4]{421} \sin{\left(\frac{\operatorname{atan}{\left(\frac{21 \sqrt{3}}{19} \right)}}{2} \right)}}{2} + \frac{\sqrt{3}}{4}\right)\right) \left(- \frac{\sqrt[4]{421} \cos{\left(\frac{\operatorname{atan}{\left(\frac{21 \sqrt{3}}{19} \right)}}{2} \right)}}{2} - \frac{1}{4} + i \left(- \frac{\sqrt[4]{421} \sin{\left(\frac{\operatorname{atan}{\left(\frac{21 \sqrt{3}}{19} \right)}}{2} \right)}}{2} - \frac{\sqrt{3}}{4}\right)\right) \left(\frac{1}{2} - \frac{\sqrt{19} i}{2}\right) \left(\frac{1}{2} + \frac{\sqrt{19} i}{2}\right)$$
=
125
$$125$$
125
Numerical answer
[src]
x1 = 0.5 - 2.17944947177034*i
x2 = -2.18708171383796 + 1.60659080584841*i
x3 = 1.68708171383796 - 0.740565402063968*i
x4 = 1.68708171383796 + 0.740565402063968*i
x5 = 0.5 + 2.17944947177034*i
x6 = -2.18708171383796 - 1.60659080584841*i
x6 = -2.18708171383796 - 1.60659080584841*i
The graph