若x2-2x+10+y2+6y=0,求(2x+y)2

题目

若x2-2x+10+y2+6y=0,求(2x+y)2

答案

x2-2x+10+y2+6y=0
x²-2x+1+y²+6y+9=0
(x-1)²+(y+3)²=0
x-1=0
y+3=0
∴x=1
y=-3
(2x+y)²=(2-3)²=1