Question

Find the solution(s) of the following equation.
\[y^3 = -343\]
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
\[y = 7\]
A
\[y = 7\]
(Choice B)
\[y = -7\]
B
\[y = -7\]
(Choice C)
\[y = 9\]
C
\[y = 9\]
(Choice D)
\[y = -9\]
D
\[y = -9\]
(Choice E) None of the above
E
None of the above

Answer 1

To solve the equation \(y^3 = -343\), we first find the cube root of \(-343\).

We can rewrite \(-343\) as:
\[
-343 = -7^3
\]

Thus, we take the cube root of both sides:
\[
y = \sqrt[3]{-343} = \sqrt[3]{-7^3} = -7
\]

The only solution to the equation is:
\[
y = -7
\]

Now, let's evaluate the choices:

- (Choice A) \(y = 7\) → Incorrect
- (Choice B) \(y = -7\) → Correct
- (Choice C) \(y = 9\) → Incorrect
- (Choice D) \(y = -9\) → Incorrect
- (Choice E) None of the above → Incorrect

The correct answer is:

(Choice B) \(y = -7\)