Tìm tất cả các cặp số nguyên x,y thỏa mãn: xy-2x+y+1=0

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Tìm tất cả các cặp số nguyên x,y thỏa mãn:
xy-2x+y+1=0

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Sarah 1 giờ 2021-09-13T07:27:47+00:00 2 Answers 0 views 0

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    0
    2021-09-13T07:29:20+00:00

    $\rm Đáp \ án:\\ (x;y)\in{(-4;3);(0;-1);(2;1);(-2;5)}\\\text{Giải thích các bước giải:}\\xy-2x+y+1=0\\⇒xy-2x+y+(3-2)=0\\⇒xy-2x+y+3-2=0\\⇒x(y-2)+y-2=-3\\⇒x(y-2)+(y-2)=-3\\⇒(y-2)(x+1)=-3\\ Ta \ có:\\-3=1.(-3)=(-3).1=(-1).3=3.(-1)\\\text{Ta có bảng sau:}\\\begin{array}{|c|c|}\hline y-2&1&-3&-1&3\\\hline x+1&-3&1&3&-1\\\hline y&3&-1&1&5\\\hline x&-4&0&2&-2\\\hline\end{array}\\ Vậy \ (x;y)\in{(-4;3);(0;-1);(2;1);(-2;5)}$

    0
    2021-09-13T07:29:29+00:00

    `xy-2x+y+1=0`

    `⇔(x+1)(y-2)=-3`

    \begin{array}{|c|c|c|}\hline x+1&1 & -1 & -3&3\\\hline y-2 &-3 & 3&1&-1\\\hline x &0 &-2 &-4&2\\\hline y&-1 &5 &3&1\\\hline\end{array}

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