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Question

Prove that 6abc<bc(b+c)+ca(c+a)+ab(a+b)

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Solution

This will be true only if a,b,c are positive
Apply AMGMfor a2b,b2a,c2a,a2c,b2c,c2b
a2b+b2a+c2a+a2c+b2c+c2b6((abc)6)16bc(b+c)+ca(c+a)+ab(a+b)6abc
Hence proved

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