Prove the following inequaltities for any positive real numbers (x, y) : (i) (x y^{3} leq frac{1}{4}
Question:
Prove the following inequaltities for any positive real numbers \(x, y\) :
(i) \(x y^{3} \leq \frac{1}{4} x^{4}+\frac{3}{4} y^{4}\)
(ii) \(x y^{3}+x^{3} y \leq x^{4}+y^{4}\).
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