6th Power

Algebra Level 3

aa+b2+bb+a2=78 \large \frac{a}{a+b^2} + \frac{b}{b+a^2} = \frac{7}{8}

Let aa and bb be positive real numbers such that their product is 22 and satisfy the equation above.

What is the value of a6+b6a^6+b^6?

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