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

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

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

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

x \geq 1

Solution steps

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

Square both sides:

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

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

Solve

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

True for all

x

True for all x

Verify Solutions:

x < 1

False

, x = 1

True

, x > 1

True

The solution is

x \geq 1

x + 3 = x + 33

- 3 x + 40 = x - 4

x + 4 = x + 4

x + 16 = x + 2

x + 21 = x - 21

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