Question

Given the equation $\sqrt{2x+1}=3$, solve for $x$ and identify if it is an extraneous solution.

Answer 1

Solve the given equation for $x$:

The given equation is, $\sqrt{2x+1}=3$.

Squaring on the both sides of the equation:

$$\begin{gathered} \therefore \left(\sqrt{2x+1}\right)=3 \\ \Rightarrow 2x+1=9 \\ \Rightarrow 2x=9-1 \\ \Rightarrow 2x=8 \\ \Rightarrow x=\frac{8}{2} \\ \Rightarrow x=4 \end{gathered}$$

Hence, the solution is $x=4$ and, it is not an extraneous root because it satisfies the original solution.