Question

Ahmed is solving the following equation for xxx.

Answer 1

Answer:

No

Step-by-step explanation:

An extraneous solution is a root of a transformed equation which is not a root of the original equation because it was not included in the domain of the original equation.

Ahmed is solving $2\sqrt[3]{x-7}+11=3$ for x.

His steps were:

$\begin{aligned}2\sqrt[3]{x-7}&=-8\\ \sqrt[3]{x-7}&=-4\\ \left(\sqrt[3]{x-7}\right)^3&=(-4)^3\\ x-7&=-64 \end{aligned}$

Since cube roots do not give two solutions when solved, it is not necessary to check his answers for extraneous solutions.