已知x^2 +5y^2 +2xy+4y+1=0,求2x+3y的值

已知x^2 +5y^2 +2xy+4y+1=0,求2x+3y的值
已知x^2 +5y^2 +2xy+4y+1=0,求2x+3y的值

已知x^2 +5y^2 +2xy+4y+1=0,求2x+3y的值
x^2 +5y^2 +2xy+4y+1=0
（x^2+2xy+y^2)+(4y^2+4y+1)=0
(x+y)^2+(2y+1)^2=0
x+y=0
2y+1=0
x=1/2
y=-1/2
则2x+3y=-1/2

x^2 +5y^2 +2xy+4y+1=0,
x^2 +2xy+y^2+4y^2 +4y+1=0,
(x+y)^2+(2y+1)^2=0
(x+y)^2=0
(2y+1)^2=0
x=-y
2y=-1,y=-1/2
x=-y=1/2
2x+3y=-2y+3y=y=-1/2

x²+2xy+y²+4y²+4y+1=0
(x+y)²+(2y+1)²=0
∵(x+y)²≥0
(2y+1)²≥0
∴x+y=0
2y+1=0
∴y=-1/2
x=1/2
∴2x+3y
=2×1/2+3×(-1/2)
=1-3/2
=-1/2

左边整理之后是（X+Y）^2+(2Y+1)^2=0所以Y=-1/2, X=1/2....
所以2X+3Y=-1/2