My idea

回答: 數學不等式 00魁北克人2015-02-06 09:05:11

Try to break y^3+y into three terms in order to use A-G inequality for 6 terms

y^3+y >= (y^3+2y^2+y)/2

The original left >= 6*xy*(1/4)^{1/6}

6*(1/4)^{1/6}>9/2

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