What is the answer to sqrt((x^2-1)^2)=x^2-1 ?

The answer to sqrt((x^2-1)^2)=x^2-1 is x = 1

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sqrt((x^2-1)^2)=x^2-1

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

x \leq - 1 or x \geq 1

Solution steps

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

Square both sides:

(x^{2} - 1)^{2} = x^{4} - 2 x^{2} + 1

(x^{2} - 1)^{2} = x^{4} - 2 x^{2} + 1

Solve

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

True for all

x

True for all x

Verify Solutions:

x < - 1

True

, x = - 1

True

, - 1 < x < 1

False

, x = 1

True

, x > 1

True

The solution is

x \leq - 1 or x \geq 1

u + 1 = u + 1

4 1 + 3 x + 6 x + 3 = - 6 x - 1

2 x - 1 = 3

4 x + 7 = 2 + 2 x

a = 21 - 2 a + 11

What is the answer to sqrt((x^2-1)^2)=x^2-1 ?
The answer to sqrt((x^2-1)^2)=x^2-1 is x<=-1\lor x>= 1
Solve for x: sqrt((x^2-1)^2)=x^2-1
The solution is x<=-1\lor x>= 1