What are the solutions to the equation x^{17}=x ?

The solutions to the equation x^{17}=x are

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x^{17}=x

x^{17} = x

Solution steps

x^{17} = x

Move

x

to the left side

x^{17} - x = 0

Factor

x^{17} - x : x (x^{4} + 2 x^{2} + 1) (x^{4} - 2 x^{2} + 1) (x^{2} + 2 x + 1) (x^{2} - 2 x + 1) (x^{2} + 1) (x + 1) (x - 1)

x (x^{4} + 2 x^{2} + 1) (x^{4} - 2 x^{2} + 1) (x^{2} + 2 x + 1) (x^{2} - 2 x + 1) (x^{2} + 1) (x + 1) (x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x^{4} + 2 x^{2} + 1 = 0 or x^{4} - 2 x^{2} + 1 = 0 or x^{2} + 2 x + 1 = 0 or x^{2} - 2 x + 1 = 0 or x^{2} + 1 = 0 or x + 1 = 0 or x - 1 = 0

Solve

x^{2} + 2 x + 1 = 0 : x = - \frac{2}{2} + i \frac{2}{2}, x = - \frac{2}{2} - i \frac{2}{2}

Solve

x^{2} - 2 x + 1 = 0 : x = \frac{2}{2} + i \frac{2}{2}, x = \frac{2}{2} - i \frac{2}{2}

Solve

x^{2} + 1 = 0 : x = i, x = - i

Solve

x + 1 = 0 : x = - 1

Solve

x - 1 = 0 : x = 1

The solutions are

x, x^{4} + y^{2} + x^{2} y^{2} + 16 x^{2} - 10 x^{2} y = 0

x, x^{3} d^{2} - x^{2} d^{1} - 3 x y = x^{2}

x^{3} - 2 x^{2} = 75

\frac{x}{3} + \frac{3}{9} = x^{4} + 75

- 3 x^{3} - 7 x + 6 = 0

What are the solutions to the equation x^{17}=x ?
The solutions to the equation x^{17}=x are
Find the zeros of x^{17}=x
The zeros of x^{17}=x are