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Question

If a, b, c >0, then prove that a3b3+b3c3+c3a33.

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Solution

We know that for a given number of real terms
A.MG.M...(1)
consider the terms to be a3b3,b3c3,c3a3
then A.M =a3b3+b3c3+c3a33
G.M =3a3b3×b3c3×c3a3=1
applying (1) a3b3+b3c3+c3a33
Hence proved

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