Tính GTNN?

E

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AD Cauchy-Schwarz, có:
$1={(x+2y)^2}={(1.x+\sqrt{2}.\sqrt{2}y)^2}$ \leq $(1+2)({x^2}+2{y^2})=3({x^2}+2{y^2})$
\Rightarrow ${x^2}+2{y^2}$ \geq $\dfrac{1}{3}$
Dấu"=" xảy ra \Leftrightarrow $x=y=\dfrac{1}{3}$
 
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