Question

tìm x\(\in Z\) để \(\dfrac{3}{\sqrt{x}-4}\in Z\)

Answer 1

\(\dfrac{3}{\sqrt{x}-4}\in Z\Leftrightarrow3⋮\sqrt{x}-4\\ \Leftrightarrow\sqrt{x}-4\inƯ\left(3\right)=\left\{-3;-1;1;3\right\}\\ \Leftrightarrow\sqrt{x}\in\left\{1;3;5;7\right\}\\ \Leftrightarrow x\in\left\{1;9;25;49\right\}\)

Answer 2

ĐK: \(x\ge0;x\ne16\)

\(\dfrac{3}{\sqrt{x}-4}\in Z\)

\(\Leftrightarrow\sqrt{x}-4\inƯ_3=\left\{\pm1;\pm3\right\}\)

\(\Leftrightarrow\sqrt{x}\inƯ_3=\left\{1;3;5;7\right\}\)

\(\Leftrightarrow x\inƯ_3=\left\{1;9;25;49\right\}\)