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

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

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

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

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

x = 0, x = 1 + 2, x = 1 - 2

Solution steps

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

Expand

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

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

Move

2

to the left side

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x^{2} - 2 x - 1 = 0

Solve

x^{2} - 2 x - 1 = 0 : x = 1 + 2, x = 1 - 2

The solutions are

x = 0, x = 1 + 2, x = 1 - 2

8 x^{3} - 12 x = 0

x^{12} - 8 x^{2} = 9

- \frac{40}{3} t^{3} + 8000 t = 5440

(x + 1) \cdot x^{3} = x + 11

(x + 4) (x + 2) (x - 3) = 0

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