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koopa
Frequent VisitorJoined: 21 Jan 2004Posts: 56
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Posted: Thu Oct 28, 2004 11:32 am Post subject: Cyclic Inequality
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Suppose, a, b, c, d > 0 Prove that: a^4*b + b^4*c + c^4*d + d^4*a >= abcd(a + b + c + d).
Please help.
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Ellen
Frequent VisitorJoined: 28 Oct 2003Posts: 197
Location: CUHK
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Posted: Thu Oct 28, 2004 11:10 pm Post subject:
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A stupid way: By AM-GM,
Similarly,
Adding these and dividing both sides by 51 gives the result.
There maybe a nicer solution though…….
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koopa
Frequent VisitorJoined: 21 Jan 2004Posts: 56
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Posted: Fri Oct 29, 2004 1:35 am Post subject:
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Wow!!! That’s a brilliant solution.
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