tìm các số nguyên x, y thoả mãn x+4xy-y=11 02/10/2021 Bởi Allison tìm các số nguyên x, y thoả mãn x+4xy-y=11
Đáp án: `x+4xy-y=11` `=> 4x+16xy-4y=44` `=> 4x.(1+4y)-(1+4y)=43` `=> (4x-1).(1+4y)=43` `=> 4x-1;1+4y in Ư(43)` Ta có bảng : $\begin{array}{|c|c|}\hline 4x-1&-43&-1&1&43\\\hline 4y+1&-1&-43&43&1\\\hline x&-\dfrac{21}{2}(\text{ktm})&0&\dfrac{1}{2}(\text{ktm}&11 \\\hline y&&-11&&0\\\hline \end{array}$Vậy `(x;y) in {(0;-11);(11;0)}` Bình luận
.
Đáp án:
`x+4xy-y=11`
`=> 4x+16xy-4y=44`
`=> 4x.(1+4y)-(1+4y)=43`
`=> (4x-1).(1+4y)=43`
`=> 4x-1;1+4y in Ư(43)`
Ta có bảng :
$\begin{array}{|c|c|}\hline 4x-1&-43&-1&1&43\\\hline 4y+1&-1&-43&43&1\\\hline x&-\dfrac{21}{2}(\text{ktm})&0&\dfrac{1}{2}(\text{ktm}&11 \\\hline y&&-11&&0\\\hline \end{array}$
Vậy `(x;y) in {(0;-11);(11;0)}`