Solve sqrt{x-1}=sqrt{2x-3}

$$\sqrt{ x-1 } = \sqrt{ 2x-3 }$$

Solve for x

$$x=2$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{x-1}\right)^{2}=\left(\sqrt{2x-3}\right)^{2}$$

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

$$x-1=\left(\sqrt{2x-3}\right)^{2}$$

Calculate \sqrt{2x-3} to the power of 2 and get 2x-3.

$$x-1=2x-3$$

Subtract 2x from both sides.

$$x-1-2x=-3$$

Combine x and -2x to get -x.

$$-x-1=-3$$

Add 1 to both sides.

$$-x=-3+1$$

Add -3 and 1 to get -2.

$$-x=-2$$

Multiply both sides by -1.

$$x=2$$

Substitute 2 for x in the equation \sqrt{x-1}=\sqrt{2x-3}.

$$\sqrt{2-1}=\sqrt{2\times 2-3}$$

Simplify. The value x=2 satisfies the equation.

$$1=1$$

Equation \sqrt{x-1}=\sqrt{2x-3} has a unique solution.

$$x=2$$