Question

For the equation $\sqrt{x+6}=x$:

Part (a): Is $x=-2$a solution?

Part (b): Is$x=3$a solution?

Short answer

Part (a): It is not a given solution.

Part (b): It is a given solution.

Step-by-step solution

Part (a) Step 1. Given information.

Consider the given equation,

$\sqrt{x+6}=x$

Part (a) Step 2. Substitute x=2 in the given equation.

Assume $x=2$and substitute it in the given equation,

localid="1647877891548" $$\begin{gathered} \sqrt{-2+6}=-2 \\ \sqrt{4}=-2 \\ 2=-2 \end{gathered}$$

It is not possible.

Hence, it is not a solution.

Part (b) Step 1. Substitute x=3 in the given equation.

Assume $x=3$and substitute it in the given equation,

localid="1647877928473" $$\begin{gathered} \sqrt{3+6}=3 \\ \sqrt{9}=3 \\ 3=3 \end{gathered}$$

It is possible.

Hence, it is a solution.