已知实数x,y满足(2x+1)^2+y^2+(y-2x)^2=1⼀3,则x+y的值?

2025-02-22 21:46:02
推荐回答(1个)
回答1:

(2x+1)^2+y^2+(y-2x)^2=1/3
4x^2+4x+1+y^2+y^2-4xy+4x^2=1/3
12x^2+6x+1+3y^2-6xy=0
(9x^2+6x+1)+(3x^2-6xy+3y^2)=0
(3x+1)^2+3(x-y)^2=0
3x+1=0,x=-1/3
x-y=0,y=x=-1/3

x+y=-1/3-1/3=-2/3