tim x y :x.y=-13 ,(x-1)(y+2)=7
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Bạn viết lại cái đề bài đi bạn tìm x, y thuộc Z và x.y
Hay là sao bạn
\(\left(y+2\right)x+\left(y+2\right)=15\Leftrightarrow\left(y+2\right)\left(x+1\right)=15\)
x+1 | 1 | 3 | 5 |
y+2 | 15 | 5 | 3 |
x | 0 | 2 | 4 |
y | 13 | 3 | 1 |
a x.y = x + y + 1992
⇔ x.y - x - y = 1992
⇔ x(y - 1) - y + 1 = 1993
⇔ x(y - 1) - (y - 1) = 1993
⇔ (y - 1)(x - 1) = 1993
TH1: \(\left\{{}\begin{matrix}y-1=1\\x-1=1993\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=2\\x=1994\end{matrix}\right.\)
TH2: \(\left\{{}\begin{matrix}y-1=1993\\x-1=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=1994\\x=2\end{matrix}\right.\)
TH3: \(\left\{{}\begin{matrix}y-1=-1\\x-1=-1993\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=0\\x=-1992\end{matrix}\right.\)
TH4: \(\left\{{}\begin{matrix}y-1=-1993\\x-1=-1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=-1992\\x=0\end{matrix}\right.\)
Vậy cặp số (x;y) thỏa mãn là: (1994;2); (2;1994); (-1992;0); (0; -1992)
\(A=5xy^2-3x^2y+6x+7y^2+1\)
\(B=13xy^2-6x^2y+3y^2+5x+5\)
=>\(A+B=18xy^2-9x^2y+11x+10y^2+6\)
\(A-B=-8xy^2+3x^2y+x+4y^2-4\)
a) Ta có: \(xy=-13\)
\(\Leftrightarrow x,y\inƯ\left(-13\right)\)
\(\Leftrightarrow x,y\in\left\{1;-1;13;-13\right\}\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left\{{}\begin{matrix}x=1\\y=-13\end{matrix}\right.\\\left\{{}\begin{matrix}x=-1\\y=13\end{matrix}\right.\\\left\{{}\begin{matrix}x=-13\\y=1\end{matrix}\right.\\\left\{{}\begin{matrix}x=13\\y=-1\end{matrix}\right.\end{matrix}\right.\)
Vậy: (x,y)∈{(1;-13);(-1;13);(-13;1);(13;-1)}
b) Ta có: \(\left(x-1\right)\left(y+2\right)=7\)
\(\Leftrightarrow x-1;y+2\inƯ\left(7\right)\)
\(\Leftrightarrow x-1;y+2\in\left\{1;7;-1;-7\right\}\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left\{{}\begin{matrix}x-1=1\\y+2=7\end{matrix}\right.\\\left\{{}\begin{matrix}x-1=7\\y+2=1\end{matrix}\right.\\\left\{{}\begin{matrix}x-1=-1\\y+2=-7\end{matrix}\right.\\\left\{{}\begin{matrix}x-1=-7\\y+2=-1\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left\{{}\begin{matrix}x=2\\y=5\end{matrix}\right.\\\left\{{}\begin{matrix}x=8\\y=-1\end{matrix}\right.\\\left\{{}\begin{matrix}x=0\\y=-9\end{matrix}\right.\\\left\{{}\begin{matrix}x=-6\\y=-3\end{matrix}\right.\end{matrix}\right.\)
Vậy: (x,y)∈{(2;5);(8;-1);(0;-9);(-6;-3)}