which statement describes how to solve $sqrt3{x^{2}-6}=sqrt3{2x + 2}$?\nsquare both sides and then solve the…

Explanation:

Step1: Analyze the cube - root equation

We have $\sqrt[3]{x^{2}-6}=\sqrt[3]{2x + 2}$. Since the cube - root function $y=\sqrt[3]{u}$ is one - to - one, if $\sqrt[3]{a}=\sqrt[3]{b}$, then $a = b$. To get rid of the cube - roots, we cube both sides.

Step2: Determine the resulting equation type

Cubing both sides of $\sqrt[3]{x^{2}-6}=\sqrt[3]{2x + 2}$ gives $x^{2}-6=2x + 2$. Rearranging this equation to the standard form $ax^{2}+bx + c = 0$, we get $x^{2}-2x-8 = 0$, which is a quadratic equation.

Answer:

C. Cube both sides and then solve the resulting quadratic equation.