Question

Tìm các sô nguyên x, y : \(x^2-2x+1-4y^2=5\)

Answer 1

\(\Leftrightarrow\left(x-1\right)^2-\left(2y\right)^2=5\)

\(\Leftrightarrow\left(x-2y-1\right)\left(x+2y-1\right)=5\)

Ta có bảng sau:

x-2y-1	-5	-1	1	5
x+2y-1	-1	-5	5	1
x	-2	-2	4	4
y	1	-1	1	-1

Vậy \(\left(x;y\right)=\left(-2;1\right);\left(-2;-1\right);\left(4;1\right);\left(4;-1\right)\)