[Toán 9]

E

eye_smile

Rg đc:
M=x−1x+y−2y+z−3zM=\dfrac{\sqrt{x-1}}{x}+\dfrac{\sqrt{y-2}}{y}+\dfrac{\sqrt{z-3}}{z}

Có: x−1+1≥2x−1x-1+1 \ge 2\sqrt{x-1}
\Rightarrow x−1x≤12\dfrac{\sqrt{x-1}}{x} \le \dfrac{1}{2}
TT có: y−2y≤122\dfrac{\sqrt{y-2}}{y} \le \dfrac{1}{2\sqrt{2}}
z−3z≤123\dfrac{\sqrt{z-3}}{z} \le \dfrac{1}{2\sqrt{3}}

\Rightarrow M≤....M \le....
Dấu "=" xảy ra \Leftrightarrow x=2;y=4;z=6x=2;y=4;z=6
 
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