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masterofmath May 6th, 2014 06:09 AM

Inequality
 
Is it true that
a/x+b/y+c/z geq 3 (a+b+c)/(x+y+z)

mathman May 6th, 2014 12:48 PM

Quote:

Originally Posted by masterofmath (Post 192998)
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).

Olinguito May 7th, 2014 09:03 AM

Quote:

Originally Posted by masterofmath (Post 192998)
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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