What are the solutions to the equation x=x^4 ?

The solutions to the equation x=x^4 are x=0,x=1,x=-1/2+(sqrt(3))/2 i,x=-1/2-(sqrt(3))/2 i

Find the zeros of x=x^4

The zeros of x=x^4 are x=0,x=1,x=-1/2+(sqrt(3))/2 i,x=-1/2-(sqrt(3))/2 i

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x = x^{4}

x = 0, x = 1, x = - \frac{1}{2} + \frac{3}{2} i, x = - \frac{1}{2} - \frac{3}{2} i

Solution steps

x = x^{4}

Switch sides

x^{4} = x

Move

x

to the left side

x^{4} - x = 0

Factor

x^{4} - x : x (x^{3} - 1)

x (x^{3} - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x^{3} - 1 = 0

Solve

x^{3} - 1 = 0 : x = 1, x = - \frac{1}{2} + \frac{3}{2} i, x = - \frac{1}{2} - \frac{3}{2} i

The solutions are

x = 0, x = 1, x = - \frac{1}{2} + \frac{3}{2} i, x = - \frac{1}{2} - \frac{3}{2} i

z^{6} = - 1

x^{3} - 3 x^{2} + x - 3 = 0

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

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

x^{3} + x^{2} - 12 x = 0

What are the solutions to the equation x=x^4 ?
The solutions to the equation x=x^4 are x=0,x=1,x=-1/2+(sqrt(3))/2 i,x=-1/2-(sqrt(3))/2 i
Find the zeros of x=x^4
The zeros of x=x^4 are x=0,x=1,x=-1/2+(sqrt(3))/2 i,x=-1/2-(sqrt(3))/2 i