在线等！！求方程x2-y2+3 x-7 y-2=0的整数解

Question

如题所述

Answer 1

x²-y²+3x-7y=2
(x+y)(x-y)+3x-7y=2
(x+y)(x-y)-2(x+y)+5(x-y)=2
(x+y)(x-y)-2(x+y)+5(x-y)-10=-8
∴(x+y+5)(x-y-2)=-8

因为x+y+5与x-y-2的奇偶性不同，
有以下四种可能
(1)x+y+5=1
x-y-2=-8
解得，x=-5，y=1

(2)x+y+5=-1
x-y-2=8
解得，x=2，y=-8

(3)x+y+5=8
x-y-2=-1
解得，x=2，y=1

(4)x+y+5=-8
x-y-2=1
解得，x=-5，y=-8

Answer 2

x²+3x=y²+7x+2
x²+3x-10=y²+7y-8
(x-5)(x-2)=(y+8)(y-1)
①当x-5=y+8=0时
x=5 y=-8
②x-5=y-1=0时
x=5 y=1
③x-2=y-8=0时
x=2 y=8
④x-2=y-1=0
x=2 y=1