What are the solutions to the equation (x-1)^3=x-1 ?

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

Find the zeros of (x-1)^3=x-1

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

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

x = 0, x = 1, x = 2

Solution steps

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

Expand

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

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

Move

1

to the right side

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

Move

x

to the left side

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

Factor

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

x (x - 1) (x - 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x - 1 = 0 or x - 2 = 0

Solve

x - 1 = 0 : x = 1

Solve

x - 2 = 0 : x = 2

The solutions are

x = 0, x = 1, x = 2

2 (x - 2)^{3} + 8 = 136

x^{3} - 11 x^{2} + 32 x - 28 = 0

3 x^{3} - 4 x^{2} + 4 x = 16

(3 - x)^{5} + (x - 5)^{5} = - 32

c, c^{1} c^{2} = r^{1} + r^{2}

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