\(4xy\le\left(x+y\right)^2\Rightarrow\left(x+y\right)^2-\left(x+y\right)\ge2\)
\(\Rightarrow\left(x+y\right)^2-\left(x+y\right)-2\ge0\)
\(\Rightarrow\left(x+y+1\right)\left(x+y-2\right)\ge0\)
\(\Rightarrow x+y-2\ge0\Rightarrow x+y\ge2\)
\(\Rightarrow A=\frac{3}{4}\left(x+y\right)+\frac{x+y}{4}+\frac{1}{x+y}\ge\frac{3}{4}.2+2\sqrt{\frac{x+y}{4\left(x+y\right)}}=\frac{5}{2}\)
\(\Rightarrow A_{min}=\frac{5}{2}\) khi \(x=y=1\)
Đúng 0
Bình luận (0)
