已知x y满足x^2+y^2-2x-y+5/4=0 求代数式xy(x+y)的值

问题补充：

已知x,y满足x^2+y^2-2x-y+5/4=0,求代数式xy(x+y)的值

答案：

解x²+y²-2x+y+5/4=0

(x²-2x+1)+(y²+y+1/4)=0

(x-1)²+(y+1/2)²=0

∴x-1=0,y+1/2=0

∴x=1,y=-1/2

∴xy(x+y)

=1×(-1/2)(1-1/2)

=-1/2×(1/2)

=-1/4