已知 x^2+xy+y^2=20 3xy+x-y=-22 求x-y的值
问题描述:
已知 x^2+xy+y^2=20 3xy+x-y=-22 求x-y的值
答
x^2+xy+y^2=203xy+x-y=-22
x^2+xy+y^2-(3xy+x-y)=20-(-22)
即x^2-2xy+y^2-(x-y)=42
(x-y)^2-(x-y)=42
(x-y)^2-(x-y)-42=0
(x-y-7)(x-y+6)=0
x-y=7或x-y=-6