Question

Tìm x nguyên để x+1⋮x²-2

Answer 1

Ta có: \(x+1⋮x^2-2\)

\(\Leftrightarrow x^2-1⋮x^2-2\)

\(\Leftrightarrow x^2-2\inƯ\left(1\right)\)

\(\Leftrightarrow x^2-2\in\left\{-1;1\right\}\)

\(\Leftrightarrow x^2\in\left\{1;3\right\}\)

mà x nguyên

nên \(x\in\left\{1;-1\right\}\)