**Problem **

For positive reals such that ,

Prove that –

**Proof**

The hypothesis implies that –

Set ,

Thus,

The inequality is now equivalent to –

Since the sum of x,y,z is 1 –

Now by AM-GM ,

Equality occurs when

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Where numbers speak …

**Problem **

For positive reals such that ,

Prove that –

**Proof**

The hypothesis implies that –

Set ,

Thus,

The inequality is now equivalent to –

Since the sum of x,y,z is 1 –

Now by AM-GM ,

Equality occurs when

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incidentally…the same solution was posted in the ineq marathon by Dimitris X …. (ofcourse..i did not see his solution) … also … an almost similar solution is given in Hojoo Lee’s Pdf..