Question

LÀM HỘ MIK BÀI 2.2 BẰNG PP CHẶN Ạ

Answer 1

Ta có:

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

Để \(A\in Z\Leftrightarrow\dfrac{3}{\sqrt{x}+2}\in Z\)

\(\Rightarrow\left(\sqrt{x}+2\right)\inƯ_{\left(3\right)}=\left\{1;-1;3;-3\right\}\)

\(\Rightarrow\sqrt{x}=\left\{-1;-3;1;-5\right\}\)

Mà \(\sqrt{x}\ge0\)

Nên \(\sqrt{x}=1\Rightarrow x=1\)

Vậy x=1 thì \(A\in Z\)