Question

Tìm x nguyên để các biểu thức sau nguyên:
a) D=\(\dfrac{11}{2-x}\) (với x≠2)

Answer 1

\(\Leftrightarrow2-x\inƯ\left(11\right)=\left\{-11;-1;1;11\right\}\\ \Leftrightarrow x\in\left\{-9;1;3;13\right\}\)

Answer 2

\(D\in Z\Rightarrow\dfrac{11}{2-x}\in Z\Rightarrow11⋮2-x\Rightarrow2-x\inƯ\left(11\right)=\left\{\pm1;\pm11\right\}\Rightarrow x\in\left\{13;3;1;-9\right\}\)