What are the solutions to the equation (x-1)^3=(x-1)^2 ?

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

Find the zeros of (x-1)^3=(x-1)^2

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

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

x = 1, x = 2

Solution steps

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

Expand

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

Expand

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

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

Move

1

to the left side

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

Move

2 x

to the left side

x^{3} - 3 x^{2} + 5 x - 2 = x^{2}

Move

x^{2}

to the left side

x^{3} - 4 x^{2} + 5 x - 2 = 0

Factor

x^{3} - 4 x^{2} + 5 x - 2 : (x - 1)^{2} (x - 2)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or x - 2 = 0

Solve

x - 1 = 0 : x = 1

Solve

x - 2 = 0 : x = 2

The solutions are

x = 1, x = 2

4 x^{4} + 17 x^{2} + 4 = 0

27 x^{4} + 21 x^{2} + 4 = 0

5 x^{5} = 25

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

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

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