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Equation:
Equation (x-3)*(x+4)=0
Equation x^3-x^2-5=0
Equation x-2(3x+2)=16
Equation x^2-1=1+(1/2)*y
Express {x} in terms of y where:
-10*x+16*y=-6
-13*x+9*y=1
-10*x+9*y=-6
-17*x+13*y=-3
Identical expressions
x^ six -(two *x- one)^ three = zero
x to the power of 6 minus (2 multiply by x minus 1) cubed equally 0
x to the power of six minus (two multiply by x minus one) to the power of three equally zero
x6-(2*x-1)3=0
x6-2*x-13=0
x⁶-(2*x-1)³=0
x to the power of 6-(2*x-1) to the power of 3=0
x^6-(2x-1)^3=0
x6-(2x-1)3=0
x6-2x-13=0
x^6-2x-1^3=0
x^6-(2*x-1)^3=O
Similar expressions
x^6+(2*x-1)^3=0
x^6-(2*x+1)^3=0

x^6-(2*x-1)^3=0 equation

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The solution

You have entered [src]

 6            3    
x  - (2*x - 1)  = 0

$$x^{6} - \left(2 x - 1\right)^{3} = 0$$

Simplify

The graph

Plot the graph f1(x)

Plot the graph f2(x)

Rapid solution [src]

x1 = 1

$$x_{1} = 1$$

             /    ___     ___ 4 ___\     ___ 4 ___
       1     |  \/ 3    \/ 2 *\/ 3 |   \/ 2 *\/ 3 
x2 = - - + I*|- ----- - -----------| - -----------
       2     \    2          2     /        2

$$x_{2} = - \frac{\sqrt{2} \sqrt[4]{3}}{2} - \frac{1}{2} + i \left(- \frac{\sqrt{2} \sqrt[4]{3}}{2} - \frac{\sqrt{3}}{2}\right)$$

             /  ___     ___ 4 ___\     ___ 4 ___
       1     |\/ 3    \/ 2 *\/ 3 |   \/ 2 *\/ 3 
x3 = - - + I*|----- - -----------| + -----------
       2     \  2          2     /        2

$$x_{3} = - \frac{1}{2} + \frac{\sqrt{2} \sqrt[4]{3}}{2} + i \left(- \frac{\sqrt{2} \sqrt[4]{3}}{2} + \frac{\sqrt{3}}{2}\right)$$

             /    ___     ___ 4 ___\     ___ 4 ___
       1     |  \/ 3    \/ 2 *\/ 3 |   \/ 2 *\/ 3 
x4 = - - + I*|- ----- + -----------| + -----------
       2     \    2          2     /        2

$$x_{4} = - \frac{1}{2} + \frac{\sqrt{2} \sqrt[4]{3}}{2} + i \left(- \frac{\sqrt{3}}{2} + \frac{\sqrt{2} \sqrt[4]{3}}{2}\right)$$

             /  ___     ___ 4 ___\     ___ 4 ___
       1     |\/ 3    \/ 2 *\/ 3 |   \/ 2 *\/ 3 
x5 = - - + I*|----- + -----------| - -----------
       2     \  2          2     /        2

$$x_{5} = - \frac{\sqrt{2} \sqrt[4]{3}}{2} - \frac{1}{2} + i \left(\frac{\sqrt{3}}{2} + \frac{\sqrt{2} \sqrt[4]{3}}{2}\right)$$

x5 = -sqrt(2)*3^(1/4)/2 - 1/2 + i*(sqrt(3)/2 + sqrt(2)*3^(1/4)/2)

Sum and product of roots [src]

sum

            /    ___     ___ 4 ___\     ___ 4 ___           /  ___     ___ 4 ___\     ___ 4 ___           /    ___     ___ 4 ___\     ___ 4 ___           /  ___     ___ 4 ___\     ___ 4 ___
      1     |  \/ 3    \/ 2 *\/ 3 |   \/ 2 *\/ 3      1     |\/ 3    \/ 2 *\/ 3 |   \/ 2 *\/ 3      1     |  \/ 3    \/ 2 *\/ 3 |   \/ 2 *\/ 3      1     |\/ 3    \/ 2 *\/ 3 |   \/ 2 *\/ 3 
1 + - - + I*|- ----- - -----------| - ----------- + - - + I*|----- - -----------| + ----------- + - - + I*|- ----- + -----------| + ----------- + - - + I*|----- + -----------| - -----------
      2     \    2          2     /        2          2     \  2          2     /        2          2     \    2          2     /        2          2     \  2          2     /        2

$$\left(\left(\left(1 + \left(- \frac{\sqrt{2} \sqrt[4]{3}}{2} - \frac{1}{2} + i \left(- \frac{\sqrt{2} \sqrt[4]{3}}{2} - \frac{\sqrt{3}}{2}\right)\right)\right) + \left(- \frac{1}{2} + \frac{\sqrt{2} \sqrt[4]{3}}{2} + i \left(- \frac{\sqrt{2} \sqrt[4]{3}}{2} + \frac{\sqrt{3}}{2}\right)\right)\right) + \left(- \frac{1}{2} + \frac{\sqrt{2} \sqrt[4]{3}}{2} + i \left(- \frac{\sqrt{3}}{2} + \frac{\sqrt{2} \sqrt[4]{3}}{2}\right)\right)\right) + \left(- \frac{\sqrt{2} \sqrt[4]{3}}{2} - \frac{1}{2} + i \left(\frac{\sqrt{3}}{2} + \frac{\sqrt{2} \sqrt[4]{3}}{2}\right)\right)$$

       /  ___     ___ 4 ___\     /  ___     ___ 4 ___\     /    ___     ___ 4 ___\     /    ___     ___ 4 ___\
       |\/ 3    \/ 2 *\/ 3 |     |\/ 3    \/ 2 *\/ 3 |     |  \/ 3    \/ 2 *\/ 3 |     |  \/ 3    \/ 2 *\/ 3 |
-1 + I*|----- + -----------| + I*|----- - -----------| + I*|- ----- + -----------| + I*|- ----- - -----------|
       \  2          2     /     \  2          2     /     \    2          2     /     \    2          2     /

$$-1 + i \left(- \frac{\sqrt{2} \sqrt[4]{3}}{2} - \frac{\sqrt{3}}{2}\right) + i \left(- \frac{\sqrt{2} \sqrt[4]{3}}{2} + \frac{\sqrt{3}}{2}\right) + i \left(- \frac{\sqrt{3}}{2} + \frac{\sqrt{2} \sqrt[4]{3}}{2}\right) + i \left(\frac{\sqrt{3}}{2} + \frac{\sqrt{2} \sqrt[4]{3}}{2}\right)$$

product

/        /    ___     ___ 4 ___\     ___ 4 ___\ /        /  ___     ___ 4 ___\     ___ 4 ___\ /        /    ___     ___ 4 ___\     ___ 4 ___\ /        /  ___     ___ 4 ___\     ___ 4 ___\
|  1     |  \/ 3    \/ 2 *\/ 3 |   \/ 2 *\/ 3 | |  1     |\/ 3    \/ 2 *\/ 3 |   \/ 2 *\/ 3 | |  1     |  \/ 3    \/ 2 *\/ 3 |   \/ 2 *\/ 3 | |  1     |\/ 3    \/ 2 *\/ 3 |   \/ 2 *\/ 3 |
|- - + I*|- ----- - -----------| - -----------|*|- - + I*|----- - -----------| + -----------|*|- - + I*|- ----- + -----------| + -----------|*|- - + I*|----- + -----------| - -----------|
\  2     \    2          2     /        2     / \  2     \  2          2     /        2     / \  2     \    2          2     /        2     / \  2     \  2          2     /        2     /

$$\left(- \frac{1}{2} + \frac{\sqrt{2} \sqrt[4]{3}}{2} + i \left(- \frac{\sqrt{2} \sqrt[4]{3}}{2} + \frac{\sqrt{3}}{2}\right)\right) \left(- \frac{\sqrt{2} \sqrt[4]{3}}{2} - \frac{1}{2} + i \left(- \frac{\sqrt{2} \sqrt[4]{3}}{2} - \frac{\sqrt{3}}{2}\right)\right) \left(- \frac{1}{2} + \frac{\sqrt{2} \sqrt[4]{3}}{2} + i \left(- \frac{\sqrt{3}}{2} + \frac{\sqrt{2} \sqrt[4]{3}}{2}\right)\right) \left(- \frac{\sqrt{2} \sqrt[4]{3}}{2} - \frac{1}{2} + i \left(\frac{\sqrt{3}}{2} + \frac{\sqrt{2} \sqrt[4]{3}}{2}\right)\right)$$

$$1$$

Numerical answer [src]

x1 = 0.4306048591021 - 0.0645794553176609*i

x2 = -1.4306048591021 + 1.79663026288654*i

x3 = 1.0

x4 = -1.4306048591021 - 1.79663026288654*i

x5 = 0.4306048591021 + 0.0645794553176609*i

x5 = 0.4306048591021 + 0.0645794553176609*i

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x^6-(2*x-1)^3=0 equation

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