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Practice problem

Intuition: Solving Equations vs. Solving Inequalities

By Thomas Ik-Hyun Kim
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Problem 3.) Let x,y,z>0x, y, z > 0; Prove that

1(x+2y)2+1(y+2z)2+1(z+2x)2≥1xy+yz+zx\frac{1}{(x+2y)^2}+\frac{1}{(y+2z)^2}+\frac{1}{(z+2x)^2} \geq\frac{1}{xy+yz+zx}

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