Question

已知x,y满足 x^2+y^2+5/4=2x+y 求(x+y)xy

Answer 1

x^2+y^2+5/4=2x+y
x^2-2x+y^2-y=-5/4
(x^2-2x+1-1)+[y^2-y+(1/2)²-(1/2)²]=-5/4
(x-1)²+(y-1/2)²-1-1/4=-5/4
所以(x-1)²+(y-1/2)²=0
因为(x-1)²>=0,(y-1/2)²>=0
所以(x-1)²=0解得x=1
(y-1/2)²=0解得y=1/2
(x+y)xy
=(1+1/2)1/2
=3/4

希望能够帮助你，有疑问欢迎追问，祝学习进步！

追问

(x^2-2x+1-1)+[y^2-y+(1/2)²-(1/2)²]=-5/4 是怎么得到的？

Answer 2

x^+y^+5/4=2x+y,

(x^2-2x+1)+(y^2-y+1/4)=0

(x-1)^2+(y-1/2)^2=0

x-1=0
y-1/2=0

x=1,y=1/2

(x+y)xy=(1+1/2)x1/2=1/3

Answer 3

第一步移项，令右边为零，再把5/4拆成1和1/4，再把x和y单独完全平方

追答