Question

2x+3y=30 .Tìm giá trị x,y nguyên biết x>0 y>0

Answer 1

Ta có: \(2x+3y=30\Leftrightarrow x=\dfrac{3}{2}\left(10-y\right)>0\)

\(\Rightarrow y< 10\Rightarrow y\in\left\{1;2;...;9\right\}\). Cũng từ \(y>0\Rightarrow10-y< 10\)

Thêm cả \(x\in Z\Rightarrow\left(10-y\right)\in B\left(2\right)=\left\{2;4;6;8\right\}\).

Suy ra: \(y\in\left\{8;6;4;2\right\}\), ứng với \(x\in\left\{3;6;9;12\right\}\).

Vậy: \(\left(x;y\right)=\left\{\left(3;8\right),\left(6;6\right),\left(9;4\right),\left(12;2\right)\right\}\)