What are the solutions to the equation x=x^5 ?

The solutions to the equation x=x^5 are x=0,x=i,x=-i,x=-1,x=1

Find the zeros of x=x^5

The zeros of x=x^5 are x=0,x=i,x=-i,x=-1,x=1

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x = x^{5}

x = 0, x = i, x = - i, x = - 1, x = 1

Solution steps

x = x^{5}

Switch sides

x^{5} = x

Move

x

to the left side

x^{5} - x = 0

Factor

x^{5} - x : x (x^{2} + 1) (x + 1) (x - 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

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 = 0, x = i, x = - i, x = - 1, x = 1

n^{3} - n^{2} - 16 n - 20 = 0

x^{3} - 8 x^{2} - 15 = 0

(x - 1) \cdot x \cdot (x + 1) = 210

20 x^{3} + 100 x^{2} + 120 x = 0

(x^{2} + 8 x + 15)^{5} = 0

What are the solutions to the equation x=x^5 ?
The solutions to the equation x=x^5 are x=0,x=i,x=-i,x=-1,x=1
Find the zeros of x=x^5
The zeros of x=x^5 are x=0,x=i,x=-i,x=-1,x=1