tìm cặp số nguyên x y biết: 2.(3-y)-x.(y-3)=19

Question

tìm cặp số nguyên x y biết: 2.(3-y)-x.(y-3)=19

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Audrey 2 tháng 2021-10-24T03:19:04+00:00 2 Answers 6 views 0

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    0
    2021-10-24T03:20:34+00:00

    Đáp án:

     

    Giải thích các bước giải:

    `2(3-y)-x(y-3)=19`

    `=> 2(3-y)+x(3-y)=19`

    `=> (3-y)(2+x)=19`

    `=> 3-y ; 2+x in Ư(19)`

    Ta có bảng :

    $\begin{array}{|c|c|}\hline 2+x&-19&-1&1&19\\\hline 3-y&-1&-19&19&1 \\\hline x&-21&-3&-1&17\\\hline y &4&22&-16&2\\\hline\end{array}$ 

    Vậy `(x;y) in {(-21;4);(-3;22);(-1;-16);(17;2)}`

    0
    2021-10-24T03:20:53+00:00

    $2(3-y)-x(y-3)=19$

    $↔2(3-y)+x(3-y)=19$

    $↔(x+2)(3-y)=19$

    $→(x+2);(3-y)∈Ư(19)=\{±1;±19\}$

    $→$ Ta có bảng

    $\begin{array}{|c|c|c|}\hline x+2&1&-1&19&-19\\\hline 3-y&19&-19&1&-1\\\hline x&-1&-3&17&-21\\\hline y&-16&22&2&4\\\hline\quad&tm&tm&tm&tm\\\hline\end{array}$

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