Question

Tìm số nguyên:
e, x+y + 3xy = 1
g, xy + 3x + y = 4

Answer 1

e) \(x+y+3xy=1\)

\(\Leftrightarrow3x+3y+9xy=3\)

\(\Leftrightarrow3x+9xy+3y=3\)

\(\Leftrightarrow3x\left(1+3y\right)+1+3y=4\)

\(\Leftrightarrow\left(3y+1\right)\left(3x+1\right)=4\)

\(\Leftrightarrow\left(3x+1\right);\left(3y+1\right)\in\left\{-1;1;-2;2;-4;4\right\}\)

\(\Leftrightarrow\left(x;y\right)\in\left\{\left(-\dfrac{2}{3};-\dfrac{5}{3}\right);\left(0;1\right);\left(-1;-1\right);\left(\dfrac{1}{3};\dfrac{1}{3}\right);\left(-\dfrac{5}{3};-\dfrac{2}{3}\right);\left(1;0\right)\right\}\)

\(\Leftrightarrow\left(x;y\right)\in\left\{\left(0;1\right);\left(-1;-1\right);\left(1;0\right)\right\}\)