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Home » Olympiad Section » Inequalities » Inequalities Unsolved Problems
 
Nice - hard with four variables
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nguyenvuthanhha
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#1
Nice - hard with four variables
Let a ; b ; c ;d be nonnegative real numbers such that : a + b + c + d = 4

Prove that :

abc + bcd + cda + dab + (abc)^2 + (bcd)^2 + (cda )^2 + (dab)^2 \ \leq \ 8


Maybe it's an old problem . I think there is no nice solution for it ( up to now) Mad
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Love the simplicity

PostPosted: Tue Oct 06, 2009 2:27 am  Back to top 
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Materazzi
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#2
Re: Nice - hard with four variables
nguyenvuthanhha wrote:
Let a ; b ; c ;d be nonnegative real numbers such that : a + b + c + d = 4

Prove that :

abc + bcd + cda + dab + (abc)^2 + (bcd)^2 + (cda )^2 + (dab)^2 \ \leq \ 8


Maybe it's an old problem . I think there is no nice solution for it ( up to now) Mad


It's easy by S.M.V my friend Wink

PostPosted: Fri Nov 06, 2009 4:09 am  Back to top 
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