Question

Mấy bạn giúp mk bài 8 với

Answer 1

\(P=\dfrac{x+1}{\sqrt{x}+1}=\dfrac{x-1+2}{\sqrt{x}+1}=\sqrt{x}-1+\dfrac{2}{\sqrt{x}+1}\)

\(=\sqrt{x}+1+\dfrac{2}{\sqrt{x}+1}-2\)

\(\Leftrightarrow P>=2\sqrt{2}-2\)

Dấu '=' xảy ra khi \(\left(\sqrt{x}+1\right)^2=2\)

\(\Leftrightarrow\sqrt{x}+1=\sqrt{2}\)

hay \(x=3-2\sqrt{2}\)