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(B) Given the equation $a^2 x^4 + b^2 y^4 = c^6$. Applying the Arithmetic Mean-Geometric Mean $(AM \geq GM)$ inequality for the two terms $a^2 x^4$ an

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$\frac{c^3}{\sqrt{2ab}}$

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(B) Given the equation $a^2 x^4 + b^2 y^4 = c^6$. Applying the Arithmetic Mean-Geometric Mean $(AM \geq GM)$ inequality for the two terms $a^2 x^4$ and $b^2 y^4$: $\frac{a^2 x^4 + b^2 y^4}{2} \geq \sqrt{(a^2 x^4)(b^2 y^4)}$ Substituting the given value $a^2 x^4 + b^2 y^4 = c^6$: $\frac{c^6}{2} \geq \sqrt{a^2 b^2 x^4 y^4}$ $\frac{c^6}{2} \geq ab x^2 y^2$ $x^2 y^2 \leq \frac{c^6}{2ab}$ Taking the square root on both sides: $xy \leq \frac{c^3}{\sqrt{2ab}}$ Thus,the maximum value of $xy$ is $\frac{c^3}{\sqrt{2ab}}$.

If $a^2 x^4 + b^2 y^4 = c^6$,then the maximum value of $xy$ is:

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