Solve sqrt{x-1}=sqrt{1-x}

$$\sqrt { x - 1 } = \sqrt { 1 - x }$$

Solve for x

$$x=1$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{x-1}\right)^{2}=\left(\sqrt{1-x}\right)^{2}$$

Calculate \sqrt{x-1} to the power of 2 and get x-1.

$$x-1=\left(\sqrt{1-x}\right)^{2}$$

Calculate \sqrt{1-x} to the power of 2 and get 1-x.

$$x-1=1-x$$

Add x to both sides.

$$x-1+x=1$$

Combine x and x to get 2x.

$$2x-1=1$$

Add 1 to both sides.

$$2x=1+1$$

Add 1 and 1 to get 2.

$$2x=2$$

Divide both sides by 2.

$$x=\frac{2}{2}$$

Divide 2 by 2 to get 1.

$$x=1$$

Substitute 1 for x in the equation \sqrt{x-1}=\sqrt{1-x}.

$$\sqrt{1-1}=\sqrt{1-1}$$

Simplify. The value x=1 satisfies the equation.

$$0=0$$

Equation \sqrt{x-1}=\sqrt{1-x} has a unique solution.

$$x=1$$