Câu hỏi của Nguyễn Phạm Ngọc Linhhh

Question

tìm các số nguyên x,y thỏa mãn :x2+3x+5=xy+2y

Nguyễn Hoàng Minh · Accepted Answer

$x^2+3x+5=xy+2y\
\Leftrightarrow x^2+3x-xy-2y+5=0\
\Leftrightarrow x\left(x+2\right)-y\left(x+2\right)+\left(x+2\right)+3=0\
\Leftrightarrow\left(x+2\right)\left(x-y+1\right)=-3=\left(-1\right)\cdot3=\left(-3\right)\cdot1$$TH_1:\left\{{}\begin{matrix}x+2=-3\x-y+1=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-5\y=-5\end{matrix}\right.\to\left(-5;-5\right)\
TH_2:\left\{{}\begin{matrix}x+2=3\x-y+1=-1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\y=3\end{matrix}\right.\to\left(1;3\right)\
TH_3:\left\{{}\begin{matrix}x+2=1\x-y+1=-3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-1\y=3\end{matrix}\right.\to\left(-1;3\right)\
TH_4:\left\{{}\begin{matrix}x+2=-1\x-y+1=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-3\y=-5\end{matrix}\right.\to\left(-3;-5\right)$Vậy $\left(x;y\right)=\left(-5;-5\right);\left(1;3\right);\left(-1;3\right);\left(-3;-5\right)$Câu trả lời: $x^2+3x+5=xy+2y\
\Leftrightarrow x^2+3x-xy-2y+5=0\
\Leftrightarrow x\left(x+2\right)-y\left(x+2\right)+\left(x+2\right)+3=0\
\Leftrightarrow\left(x+2\right)\left(x-y+1\right)=-3=\left(-1\right)\cdot3=\left(-3\right)\cdot1$$TH_1:\left\{{}\begin{matrix}x+2=-3\x-y+1=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-5\y=-5\end{matrix}\right.\to\left(-5;-5\right)\
TH_2:\left\{{}\begin{matrix}x+2=3\x-y+1=-1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\y=3\end{matrix}\right.\to\left(1;3\right)\
TH_3:\left\{{}\begin{matrix}x+2=1\x-y+1=-3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-1\y=3\end{matrix}\right.\to\left(-1;3\right)\
TH_4:\left\{{}\begin{matrix}x+2=-1\x-y+1=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-3\y=-5\end{matrix}\right.\to\left(-3;-5\right)$Vậy $\left(x;y\right)=\left(-5;-5\right);\left(1;3\right);\left(-1;3\right);\left(-3;-5\right)$

\(\left(x-2\right)\left(y+1\right)\)	\(x-2\)	\(y+1\)	\(x\)	\(y\)
\(1\)	\(1\)	\(1\)	\(3\)	\(0\)
\(1\)	\(-1\)	\(-1\)	\(1\)	\(-2\)

x	1	-1	11	-11
y+1	11	-11	1	-1
y	10	-12	0	-2

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y+3	-3	-1	1	3
y	-6	-4	-2	0
x-1	-1	-3	3	1
x	0	-2	4	2

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