Question

tìm x nguyên để \(\left|\dfrac{\sqrt{x}-2}{\sqrt{x}+1}\right|+\dfrac{\sqrt{x}-2}{\sqrt{x}+1}=0\)

Answer 1

\(\left|\dfrac{\sqrt{x}-2}{\sqrt{x}+1}\right|+\dfrac{\sqrt{x}-2}{\sqrt{x}+1}=0\left(x\ge0\right)\)

\(\Leftrightarrow\left|\dfrac{\sqrt{x}-2}{\sqrt{x}+1}\right|=-\left(\dfrac{\sqrt{x}-2}{\sqrt{x}+1}\right)\)

\(\Leftrightarrow\dfrac{\sqrt{x}-2}{\sqrt{x}+1}\le0\)

\(\Leftrightarrow\sqrt{x}-2\le0\left(\sqrt{x}+1>0\right)\)

\(\Leftrightarrow\sqrt{x}\le2\)

\(\Leftrightarrow x\le4\) kết hợp \(x\ge0\Rightarrow0\le x\le4\)

mà \(x\in Z\)

\(\Rightarrow x\in\left\{0;1;2;3;4\right\}\)