Question

tìm các số nguyên x,y biết:

2x²-2xy=5x-y-19

giúp mk vs mai nộp rùi

Answer 1

ta co:2x^2-2xy=5x-y-19

2xy-2x^2=-5x+y+19   2xy-y=2x^2-5x+19   y(2x-1)=2x^2-5x+19 y=2x^2-5x+19/2x-1 y thuoc z thi 2x^2-5x+19chia het cho 2x-1 hay (2x-1)(x-2)+17 chia het cho 2x-1 suy ra 17 chia het cho 2x-1 say ra 2x-1 thuoc uoc cua 7 suy ra 2x-1 thuoc -1,1,7,-7 suy ra x=0,x=1,x=4,x=-3 voi x=0 suy ra y=-19 x=1 suy ra y=16 x=4 suy ra y=31/7(loai) x=-3 suy ra y=-52/7(loai) vay cac cap so nguyen (x;y)can tim la (1,16);(0,-19)