If a,b,c are real and distinct , then show that a2(1+b2) + b2(1+c2) +c2(1+a2) > 6abc 

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Please find below the solution to the asked query:

we know that for positive numbersArithmetic MeanGeometric Meana2+a2b2+b2+b2c2+c2+c2a26a2.a2b2.b2.b2c2.c2.c2a26a21+b2+b21+c2+c21+a26a6.b6c66a21+b2+b21+c2+c21+a26abca21+b2+b21+c2+c21+a26abc Answer

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