Question

Ahmed is solving the following equation for xxx.

2\sqrt[3]{x-7}+11=32
3

x−7
​
+11=32, cube root of, x, minus, 7, end cube root, plus, 11, equals, 3
His first few steps are given below.
\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}
2
3

x−7
​

3

x−7
​

(
3

x−7
​
)
3

x−7
​

=−8
=−4
=(−4)
3

=−64
​

Is it necessary for Ahmed to check his answers for extraneous solutions?
Choose 1 answer:

Answer 1

no

Explanation:

Answer 2

No

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.