Cho $x+y+z=1$. tìm GTLN $\frac{x}{x+2016}+\frac{y}{y+2016}+\frac{z}{z+2016}$
Edited by tpdtthltvp, 27-05-2016 - 12:46.
tìm GTLN $\frac{x}{x+2016}+\frac{y}{y+2016}+\frac{z}{z+2016}$
Started By anna111176, 27-05-2016 - 12:09
#2
Posted 27-05-2016 - 13:10
minhquanym
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Binh nhất
$\frac{x}{x+2016}=1-\frac{2016}{x+2016}$ Lại có $\sum \frac{1}{x+2016} \geq \frac{9}{x+y+z+6048} = \frac{9}{6049}$
=> $\sum \frac{x}{x+2016}$ $\leq$ 3- $\frac{18144}{6049}$
Dấu = xảy ra khi x=y=z=1/3
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