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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 nonnegative).
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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