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August 19th, 2013, 06:17 AM   #1
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Inequality

Is this statement true
for any x,y side of triangle
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August 19th, 2013, 08:17 AM   #2
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Re: Inequality

Quote:
Originally Posted by masterofmath
for any x,y side of triangle
That doesn't make sense. Any x,y are sides of a triangle. But not every x,y,z is that, but that's not the matter.
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August 19th, 2013, 10:55 AM   #3
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Re: Inequality

Actually the inequality is true for every positive x and y.
Using arithmetic harmonic mean inequality we have





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August 21st, 2013, 04:17 AM   #4
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Re: Inequality

"Solution: 1/(2y+x)+1/(2x+y)=4/(x+y)
if x, y side of triangle then this statement is not true."
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August 21st, 2013, 04:49 AM   #5
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It's true if x = y and you have minus (instead of plus) signs in the denominators on the left-hand side. Nobody has suggested it works with the plus signs!
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August 21st, 2013, 11:59 AM   #6
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Re: Inequality

So what is the final solution?!
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August 21st, 2013, 12:21 PM   #7
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Re: Inequality

Quote:
Originally Posted by crom
the inequality is true for every positive x and y.
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