Question

[bùi hoàng yến]

tìm nghiệm nguyên của pt

x\(^2\)-xy=6x-5y-8

Answer 1

[Trần Minh Hoàng]

Ta có:

\(x^2-xy=6x-5y-8\)

\(\Leftrightarrow x\left(x-y\right)-5\left(x-y\right)=x-8\)

\(\Leftrightarrow\left(x-5\right)\left(x-y\right)-\left(x-5\right)=-3\)

\(\Leftrightarrow\left(x-5\right)\left(x-y-1\right)=-3\)

Ta có bảng sau:

x - 5	-1	-3	1	3
x - y - 1	3	1	-3	-1
x	4	2	6	8
y	0	0	8	8

Vậy...

Answer 2

[Trần Quốc Lộc]

\(x^2-xy=6x-5y-8\\ \Leftrightarrow\left(x^2-5x\right)-\left(xy-5y\right)-\left(x-5\right)=-3\\ \Leftrightarrow x\left(x-5\right)-y\left(x-5\right)-\left(x-5\right)=-3\\ \Leftrightarrow\left(x-y-1\right)\left(x-5\right)=-3\\ =\left(-1\right)\cdot3=3\cdot\left(-1\right)=1\cdot\left(-3\right)=\left(-3\right)\cdot1\)

Do \(x;y\in Z\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-y-1=-1\\x-5=3\end{matrix}\right.\\\left\{{}\begin{matrix}x-y-1=3\\x-5=-1\end{matrix}\right.\\\left\{{}\begin{matrix}x-y-1=1\\x-5=-3\end{matrix}\right.\\\left\{{}\begin{matrix}x-y-1=-3\\x-5=1\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}8-y-1=-1\\x=8\end{matrix}\right.\\\left\{{}\begin{matrix}4-y-1=3\\x=4\end{matrix}\right.\\\left\{{}\begin{matrix}2-y-1=1\\x=2\end{matrix}\right.\\\left\{{}\begin{matrix}6-y-1=-3\\x=6\end{matrix}\right.\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=8\\y=8\end{matrix}\right.\\\left\{{}\begin{matrix}x=4\\y=0\end{matrix}\right.\\\left\{{}\begin{matrix}x=2\\y=0\end{matrix}\right.\\\left\{{}\begin{matrix}x=6\\y=8\end{matrix}\right.\end{matrix}\right.\)

Vậy pt có tập nghiệm nguyên \(\left\{x;y\right\}=\left\{8;8\right\};\left\{4;0\right\};\left\{2;0\right\};\left\{6;8\right\}\)