已知(x+y)(x+y-10)+25=0,且x-y=3,求x,y的值.

问题描述:

已知(x+y)(x+y-10)+25=0,且x-y=3,求x,y的值.

设x+y=a,则a(a-10)+25=0,
即a2-10a+25=0,(a-5)2=0,
∴a-5=0,
则a=5,即x+y=5,
根据题意得:

x+y=5
x−y=3

解得:
x=4
y=1