Question

Giúp em ;-;

Answer 1

\(3=x+y=\dfrac{x}{2}+\dfrac{x}{2}+y\ge3\sqrt[3]{\dfrac{x}{2}.\dfrac{x}{2}.y}=3\sqrt[3]{\dfrac{x^2y}{4}}\)

\(\Rightarrow\sqrt[3]{\dfrac{x^2y}{4}}\le1\Leftrightarrow\dfrac{x^2y}{4}\le1\Leftrightarrow x^2y\le4\) (đpcm)

Dấu "=" xảy ra khi \(\left(x;y\right)=\left(2;1\right)\)