What are the solutions to the equation (x^2-2x)^2=x^2 ?

The solutions to the equation (x^2-2x)^2=x^2 are x=0,x=1,x=3

Find the zeros of (x^2-2x)^2=x^2

The zeros of (x^2-2x)^2=x^2 are x=0,x=1,x=3

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

x = 0, x = 1, x = 3

Solution steps

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

Expand

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

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

Move

x^{2}

to the left side

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x - 1 = 0 or x - 3 = 0

Solve

x - 1 = 0 : x = 1

Solve

x - 3 = 0 : x = 3

The solutions are

x = 0, x = 1, x = 3

20 x^{3} - 24 x^{2} = 0

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

(x^{3} + 1)^{3} - 16 x + 8 = 0

5 x^{3} + 7 x^{2} - 11 x + 3 = 0

z^{4} = - 2 + 23 i

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