Question

Tìm x,y nguyên dương thỏa mản 

(2x+5).(y-3)=22

Answer 1

\(\left(2x+5\right)\left(y-3\right)=22\\ \Rightarrow\left(2x+5\right);\left(y-3\right)\inƯ\left(22\right)=\left\{1;2;11;22\right\}\\ TH1:2x+5=1\Rightarrow x=-2\left(loại\right);\left(y-3\right)=22\Rightarrow y=25\\ TH2:2x+5=2\Rightarrow x=-\dfrac{3}{2}\left(loại\right);\left(y-3\right)=11\Rightarrow y=14\\ TH3:2x+5=11\Rightarrow x=3;\left(y-3\right)=2\Rightarrow y=5\\ TH4:2x+5=22\Rightarrow x=\dfrac{17}{2}\left(loại\right);\left(y-3\right)=1\Rightarrow y=4\\Vậy:\left(x;y\right)=\left(3;5\right)\)

Answer 2

(2x + 5)(y - 3) = 22

Ư(22) = {-1,-2,-11,-22,1,2,11,22}

=> Ta có bảng:

2x+5	-1	-2	-11	-22	1	2	11	22
y-3	-22	-11	-2	-1	22	11	2	1
x	-3	-7/2	-8	-27/2	-2	-3/2	3	17/2
y	-19	-8	1	2	25	14	5	4

Vậy ta có cặp x,y nguyên dương thỏa mãn là: (3;5)