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 January 19th, 2012, 11:22 AM #1 Member   Joined: Jun 2010 Posts: 35 Thanks: 0 Prove this inequality Let $a,b,c$ be positive integers that $a+b+c>a_1+b_1+c_1$. Prove this inequality: $\sqrt[n]{a}+\sqrt[n]{b}+\sqrt[n]{c}>\sqrt[n]{a_1}+\sqrt[n]{b_1}+\sqrt[n]{c_1}$. But if $a,b,c$ are real positive numbers? Please put a step-by-step proof.
January 19th, 2012, 11:45 AM   #2
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Re: Prove this inequality

Quote:
 Originally Posted by Phatossi Let $a,b,c$ be positive integers that $a+b+c>a_1+b_1+c_1$. Prove this inequality: $\sqrt[n]{a}+\sqrt[n]{b}+\sqrt[n]{c}=\sqrt[n]{a_1}+\sqrt[n]{b_1}+\sqrt[n]{c_1}$. But if $a,b,c$ are real positive numbers? Please put a step-by-step proof.
I don't see an inequality.

 January 19th, 2012, 10:54 PM #3 Member   Joined: Jun 2010 Posts: 35 Thanks: 0 Re: Prove this inequality I did a mistake while posting it in latex, now I have edited it.

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