Question

hãy chứng minh 

Answer 1

\(4\le\left(\sqrt{x}+1\right)\left(\sqrt{y}+1\right)\le\dfrac{1}{4}\left(\sqrt{x}+\sqrt{y}+2\right)^2\le\dfrac{1}{4}\left(\sqrt{2\left(x+y\right)}+2\right)^2\)

\(\Rightarrow\sqrt{2\left(x+y\right)}+2\ge4\)

\(\Rightarrow2\left(x+y\right)\ge4\)

\(\Rightarrow x+y\ge2\)