Question

solve each radical equation (check your solutions!!!

1. \\(sqrt{2x} = sqrt{x + 4}\\)

Explanation:

Step1: Square both sides

To eliminate the square roots, we square both sides of the equation \(\sqrt{2x}=\sqrt{x + 4}\). Squaring a square root cancels them out, so we get \((\sqrt{2x})^2=(\sqrt{x + 4})^2\), which simplifies to \(2x=x + 4\).

Step2: Solve for x

Subtract \(x\) from both sides of the equation \(2x=x + 4\). So, \(2x-x=x + 4-x\), which gives \(x = 4\).

Step3: Check the solution

We substitute \(x = 4\) back into the original equation to verify. For the left - hand side, \(\sqrt{2x}=\sqrt{2\times4}=\sqrt{8}=2\sqrt{2}\). For the right - hand side, \(\sqrt{x + 4}=\sqrt{4 + 4}=\sqrt{8}=2\sqrt{2}\). Since the left - hand side equals the right - hand side when \(x = 4\), the solution is valid.

Answer:

\(x = 4\)