已知x,y满足 x^2+y^2+5/4=2x+y 求(x+y)xy
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已知x,y满足 x^2+y^2+5/4=2x+y 求(x+y)xy
已知x,y满足 x^2+y^2+5/4=2x+y 求(x+y)xy
已知x,y满足 x^2+y^2+5/4=2x+y 求(x+y)xy
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!
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
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 全部展开 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 收起