6th Power

Algebra Level 3

\[ \large \frac{a}{a+b^2} + \frac{b}{b+a^2} = \frac{7}{8} \]

Let \(a\) and \(b\) be positive real numbers such that their product is \(2\) and satisfy the equation above.

What is the value of \(a^6+b^6\)?

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