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 May 6th, 2014, 06:09 AM #1 Newbie   Joined: May 2013 Posts: 26 Thanks: 0 Inequality Is it true that a/x+b/y+c/z geq 3 (a+b+c)/(x+y+z)
May 6th, 2014, 12:48 PM   #2
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Quote:
 Originally Posted by masterofmath Is it true that a/x+b/y+c/z geq 3 (a+b+c)/(x+y+z)
As a minimum you need some restrictions on x,y,z (all non-negative).

May 7th, 2014, 09:03 AM   #3
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Quote:
 Originally Posted by masterofmath Is it true that $\dfrac ax + \dfrac by + \dfrac cz \geq \dfrac{3 (a+b+c)}{x+y+z}$
$$\frac12 + \frac23 + \frac12\, =\, \frac{35}{21}\ <\ \frac{36}{21} \, = \, \frac{3(1+2+1)}{2+3+2}$$

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