Cho x, y, z >0 va khong co hai so dong thoi bang khong. Tim GTNN cua bieu thuc:
P = $\sqrt{\dfrac{x+2y}{x+2z}}$ + $\sqrt{\dfrac{y+2z}{y+2x}}$ + $\sqrt{\dfrac{z+2x}{z+2y}}$
GTNN
Started By picachu113, 10-03-2011 - 00:07
#1
Posted 10-03-2011 - 00:07
#2
Posted 10-03-2011 - 00:10
[quote name='picachu113' date='Mar 9 2011, 11:07 AM' post='254598']
Cho $x, y, z >0$ va "khong co hai so dong thoi bang khong"?(Hơi thừa)!
. Tim GTNN cua bieu thuc:
P = $\sqrt{\dfrac{x+2y}{x+2z}}+\sqrt{\dfrac{y+2z}{y+2x}}+\sqrt{\dfrac{z+2x}{z+2y}}$
Cho $x, y, z >0$ va "khong co hai so dong thoi bang khong"?(Hơi thừa)!
. Tim GTNN cua bieu thuc:
P = $\sqrt{\dfrac{x+2y}{x+2z}}+\sqrt{\dfrac{y+2z}{y+2x}}+\sqrt{\dfrac{z+2x}{z+2y}}$
"Phong độ là nhất thời, đẳng cấp là mãi mãi"!!!
#3
Posted 10-03-2011 - 00:15
Cho $x, y, z >0$ va "khong co hai so dong thoi bang khong"?(Hơi thừa)!
. Tim GTNN cua bieu thuc:
P = $\sqrt{\dfrac{x+2y}{x+2z}}+\sqrt{\dfrac{y+2z}{y+2x}}+\sqrt{\dfrac{z+2x}{z+2y}}$
$P=\sum\dfrac{x+2y}{\sqrt{(x+2y)(x+2z)} }\geq \sum \dfrac{x+2y}{\dfrac{x+2y+x+2z}{2} }=3$(AM-GM)
Em tự tìm dấu "=" nhé!
. Tim GTNN cua bieu thuc:
P = $\sqrt{\dfrac{x+2y}{x+2z}}+\sqrt{\dfrac{y+2z}{y+2x}}+\sqrt{\dfrac{z+2x}{z+2y}}$
$P=\sum\dfrac{x+2y}{\sqrt{(x+2y)(x+2z)} }\geq \sum \dfrac{x+2y}{\dfrac{x+2y+x+2z}{2} }=3$(AM-GM)
Em tự tìm dấu "=" nhé!
Edited by khacduongpro_165, 10-03-2011 - 00:16.
"Phong độ là nhất thời, đẳng cấp là mãi mãi"!!!
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