已知x2+y2-6x+4y+13=0,求2x+3y

问题描述:

已知x2+y2-6x+4y+13=0,求2x+3y

x^2+y^2-6x+4y+13=0
(x-3)^2+(y+2)^2=0
x=3 y=-2
2x+3y=2*3-2*3=0

x2+y2-6x+4y+13=0
(x-3)²+(y+2)²=0
x=3,y=-2
2x+3y
=2×3+3×(-2)
=0

即(x²-6x+9)+(y²+4y+4)=0
(x-3)²+(y+2)²=0
所以x-3=y+2=0
所以x=3,y=-2
所以2x+3y
=6-6
=0