Question

So sánh \(\frac{\sqrt{x}-2}{\sqrt{x}+1}với\frac{-5}{2}\)

Answer 1

ĐKXĐ: \(x\ge0\)

Xét:

\(\frac{\sqrt{x}-2}{\sqrt{x}+1}-\left(\frac{-5}{2}\right)=\frac{\sqrt{x}-2}{\sqrt{x}+1}+\frac{5}{2}=\frac{2\left(\sqrt{x}-2\right)+5\left(\sqrt{x}+1\right)}{2\left(\sqrt{x}+1\right)}=\frac{7\sqrt{x}+1}{2\left(\sqrt{x}+1\right)}>0,\forall x\ge0\\ \Rightarrow\frac{\sqrt{x}-2}{\sqrt{x}+1}>\frac{-5}{2},\forall x\ge0\)