已知x2+4y2+z2-2x+4y-6z+11=0 求x+y+z的值

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已知x2+4y2+z2-2x+4y-6z+11=0 求x+y+z的值

已知x2+4y2+z2-2x+4y-6z+11=0 求x+y+z的值
已知x2+4y2+z2-2x+4y-6z+11=0 求x+y+z的值

已知x2+4y2+z2-2x+4y-6z+11=0 求x+y+z的值

x^2+4y^2+z^2-2x+4y-6z+11=0
(x²-2x+1)+(4y²+4y+1)+(z²-6z+9)=0
(x-1)²+(2y+1)²+(z-3)²=0
得:
x-1=0且2y+1=0且z-3=0
则:x=1、y=-1/2、z=3
x+y+z=7/2

由x2+4y2+z2-2x+4y-6z+11=0
则(x-1)^2+(2y+1)^2+(z-3)^2=0
则x=1,y=-1/2,z=3
则x+y+z=7/2

x^2+4y^2+z^2-2x+4y-6z+11
=(x-1)^2+(2y+1)^2+(z-3)^2
=0,得
x=1,y=-1/2,z=3
x+y+z=1-1/2+3=7/2