Question

Tìm các cặp số nguyên thỏa mãn 

x²+2y²-3xy+2x-4y+3=0

Answer 1

\(x^2+2y^2-3xy+2x-4y+3=0\)

\(\Leftrightarrow\left(x^2-3xy+\frac{9}{4}y^2\right)+2\left(x-\frac{3}{2}y\right)+1-\left(\frac{1}{4}y^2+y+1\right)+3=0\)

\(\Leftrightarrow\left(x-\frac{3}{2}y\right)^2+2\left(x-\frac{3}{2}y\right)+1-\left(\frac{1}{2}y+1\right)^2+3=0\)

\(\Leftrightarrow\left(x-\frac{3}{2}y+1\right)^2-\left(\frac{1}{2}y+1\right)^2=-3\)

\(\Leftrightarrow\left(x-\frac{3}{2}y+1-\frac{1}{2}y-1\right)\left(x-\frac{3}{2}y+1+\frac{1}{2}y+1\right)=-3\)

\(\Leftrightarrow\left(x-2y\right)\left(x-y+2\right)=-3\)

Đến đây tự làm ( Dễ )