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

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

Solve for x

$$x=3$$

Solution Steps

Square both sides of the equation.

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

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

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

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

$$2x-1=x+2$$

Subtract x from both sides.

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

Combine 2x and -x to get x.

$$x-1=2$$

Add 1 to both sides.

$$x=2+1$$

Add 2 and 1 to get 3.

$$x=3$$

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

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

Simplify. The value x=3 satisfies the equation.

$$5^{\frac{1}{2}}=5^{\frac{1}{2}}$$

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

$$x=3$$