Q. 342 - Intermediate Algebra

Question

In the following exercises, solve. $\sqrt{x+5}-\sqrt{x-3}=2$

Step-by-Step Solution

Answer

The solution of the radical equation is $x=4.$

Step 1. Given Information

$\sqrt{x+5}-\sqrt{x-3}=2$

$\sqrt{x+5}=2+\sqrt{x-3}$

Step 2. The radical on the right is isolated. Square both sides.

${\left(\sqrt{x+5}\right)}^2={\left(2+\sqrt{x-3}\right)}^2$

Simplify$$\begin{gathered} x+5=4+\left(x-3\right)+4\sqrt{x-3} \\ x+5-4-x+3=4\sqrt{x-3} \\ 4=4\sqrt{x-3} \\ 1=\sqrt{x-3} \end{gathered}$$

Step 3. Square both sides

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

simplify

$x=4$