Question
[SOUTHDOWNS COLLEGE]Solve for \( x \) if \( (x+2)^{\frac{1}{3}}=-2 \)
Ask by Maxwell Boyd. in South Africa
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x = -10 \)
Solution
1. Start with the equation:
\[
(x+2)^{\frac{1}{3}} = -2
\]
2. Cube both sides to eliminate the cube root:
\[
\left((x+2)^{\frac{1}{3}}\right)^3 = (-2)^3
\]
3. Simplify both sides:
\[
x+2 = -8
\]
4. Solve for \( x \):
\[
x = -8 - 2
\]
\[
x = -10
\]
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Simplify this solution Bonus Knowledge
To solve the equation \( (x+2)^{\frac{1}{3}} = -2 \), you start by cubing both sides to eliminate the cube root. This gives you: \[ x + 2 = (-2)^3 \] Calculating the right side, you find: \[ x + 2 = -8 \] Next, subtract 2 from both sides to isolate \( x \): \[ x = -8 - 2 \] \[ x = -10 \] So the solution to the equation is \( x = -10 \).
