https://file.aiquickdraw.com/mathbot/file/17278754985302ler35dx.jpg

The equation to solve is:

\[
(1 + x)^{2/3} + (1 - x)^{2/3} = 4(1 - x^2)^{1/3}
\]

Let's break it down step-by-step to find the values of \(x\).

### Step 1: Simplify the equation
First, rewrite the equation:
\[
(1 + x)^{2/3} + (1 - x)^{2/3} = 4 \cdot (1 - x^2)^{1/3}
\]

Since \((1 - x^2) = (1 + x)(1 - x)\), we can express the equation as:
\[
(1 + x)^{2/3} + (1 - x)^{2/3} = 4 \cdot \left( (1 + x)(1 - x) \right)^{1/3}
\]

The right-hand side simplifies to:
\[
4 \cdot \left( (1 + x)(1 - x) \right)^{1/3} = 4 \cdot \left( (1 + x)(1 - x) \right)^{1/3}
\]
\[
= 4 \cdot \left( (1 + x^2) \right)^{1/3}
\]
.
Then simplifying

Solving equation (1+x)^(2/3) + (1-x)^(2/3) = 4(1-x^2)^(1/3), find values of x

Step-by-step solution for solving the algebraic equation (1+x)^(2/3) + (1-x)^(2/3) = 4(1-x^2)^(1/3). This example covers key concepts in algebra and exponent simplification. Suitable for advanced high school students in Grades 11-12.

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