Question

Tìm x để \(\dfrac{\sqrt{x}+5}{\sqrt{x}+2}\) < 2

Answer 1

\(\dfrac{\sqrt{x}+5}{\sqrt{x}+2}=1+\dfrac{3}{\sqrt{x}+2}< 2\)

\(\Leftrightarrow\dfrac{3}{\sqrt{x}+2}< 1\Leftrightarrow\sqrt{x}+2>3\Leftrightarrow\sqrt{x}>1\)

\(\Leftrightarrow x>1\)

Answer 2

\(\Rightarrow\sqrt{x}+5< 2\left(\sqrt{x}+2\right)\Rightarrow\sqrt{x}+5-2\sqrt{x}-4< 0\)

\(\Rightarrow-\sqrt{x}+1< 0\Rightarrow-\sqrt{x}< -1\Rightarrow\sqrt{x}>1\Rightarrow x>1\)