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Prove that a^4+b^4+c^4> a b c(a+b+c),w h...

Prove that `a^4+b^4+c^4> a b c(a+b+c),w h e r ea ,b ,c > 0.`

Text Solution

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`(a^4+b^4+c^4)/(3)gt((a+b+c)/(3))^4`
`=((a+b+c)/(3))((a+b+c)/(3))^3 `
Now,
`(a+b+c)/(3)gt (abc)^(1//3) or ((a+b+c)/(3)^3 gt abc`
`rArr (a^4+b^4+c^4)/(3)gt((a+b+c)/(3))abc`
or `a^4+b^4+c^4 gt abc (a+b+c)`.
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