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Prove that the greatest value of `x y` is `c^3//sqrt(2a b)dot` if `a^2x^4+b^4y^4=c^6dot`

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To prove that the greatest value of \( xy \) is \( \frac{c^3}{\sqrt{2ab}} \) given the condition \( a^2x^4 + b^2y^4 = c^6 \), we can use the Arithmetic Mean-Geometric Mean (AM-GM) inequality. ### Step-by-Step Solution: 1. **Start with the given equation**: \[ a^2x^4 + b^2y^4 = c^6 \] ...
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