Question

chứng tỏ \(\frac{\sqrt{x}+2}{\sqrt{x}+1}\)< hoặc = 2

Answer 1

DKXD x\(\ge0\)

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

voi moi x lon hon bang 0 ta luon co \(\sqrt{x}\ge0\Rightarrow\sqrt{x}+1\ge1\Rightarrow\frac{1}{\sqrt{x}+1}\le1\Rightarrow1+\frac{1}{\sqrt{x}+1}\le1\Rightarrow dpcm\)