Question

Tìm các số nguyên x,y thỏa mãn: (x-1)(4-x)=|y-1|+2

Answer 1

Do \(\left|y-1\right|+2\ge2\Rightarrow\left(x-1\right)\left(4-x\right)\ge2\)

\(\Rightarrow-x^2+5x-6\ge0\\ \Rightarrow\left(3-x\right)\left(x-2\right)\ge0\\ \Rightarrow2\le x\le3\)

Mà \(x\in Z\Rightarrow x\in\left\{2;3\right\}\)

Với \(x=2\Rightarrow\left|y-1\right|+2=2\Rightarrow\left|y-1\right|=0\Rightarrow y=1\)

Với \(x=3\Rightarrow\left|y-1\right|+2=3\Rightarrow\left|y-1\right|=1\Rightarrow\left[{}\begin{matrix}y=2\\y=0\end{matrix}\right.\)

Vậy PT có nghiệm \(\left(x;y\right)\) là \(\left(2;1\right);\left(3;2\right);\left(3;0\right)\)