What are the solutions to the equation x^6=x ?

The solutions to the equation x^6=x are x=0,x=1

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x^6=x

x^{6} = x

x = 0, x = 1

Solution steps

x^{6} = x

Move

x

to the left side

x^{6} - x = 0

Factor

x^{6} - x : x (x - 1) (x^{4} + x^{3} + x^{2} + x + 1)

x (x - 1) (x^{4} + x^{3} + x^{2} + x + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x - 1 = 0 or x^{4} + x^{3} + x^{2} + x + 1 = 0

Solve

x - 1 = 0 : x = 1

Solve

x^{4} + x^{3} + x^{2} + x + 1 = 0 :

No Solution for

x \in R

The solutions are

x = 0, x = 1

y^{4} - 37 y^{2} + 36 = 0

(m^{2} - 10 m + 29)^{2} = 0

x^{3} - 4 x^{2} - 25 x + 100 = 0

(2 x - x^{2})^{5} = 0

4 x^{6} - 19 x^{4} + 11 x^{2} + 4 = 0

What are the solutions to the equation x^6=x ?
The solutions to the equation x^6=x are x=0,x=1
Find the zeros of x^6=x
The zeros of x^6=x are x=0,x=1