已知x、y满足x^2+y^2-4x+y+17/4=0,求(x+y)^2的值

已知x、y满足x^2+y^2-4x+y+17/4=0,求(x+y)^2的值
已知x、y满足x^2+y^2-4x+y+17/4=0,求(x+y)^2的值

已知x、y满足x^2+y^2-4x+y+17/4=0,求(x+y)^2的值
x^2+y^2-4x+y+17/4=0
x²-4x+4+y²+y+1/4=0
(x-2)²+(y+1/2)²=0
∴x-2=0 y+1/2=0
x=2 y=-1/2
∴(x+y)²=(2-1/2)²=(3/2)²=9/4