What are the solutions to the equation (x-1)(x^2-2)=(x-1)(x-2) ?

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

Find the zeros of (x-1)(x^2-2)=(x-1)(x-2)

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

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

x = 0, x = 1

Solution steps

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

Move

(x - 1) (x - 2)

to the left side

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x - 1 = 0

Solve

x - 1 = 0 : x = 1

The solutions are

x = 0, x = 1

2 x^{3} - 13 x^{2} + 36 = 0

x^{3} + 3 x^{2} - 10 x = 0

x^{3} + 512 = 0

4 x^{3} - 25 x = 0

0 = 18 x^{4} + 87 x^{3} + 3 x^{2} - 108 x

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