若3x+2y+z=1,2x+y+3z=2,x+3y+2z=3.求x+y+z的值

2025-01-02 16:04:21
推荐回答(5个)
回答1:

三个式子相加,得6x+6y+6z=6,从而x+y+z=1

回答2:

6x+6y+6z=6,从而x+y+z=1

回答3:

z

回答4:

等于1

回答5:

解:
x-3=y-2 x-y=1
y-2=z-1 y-z=1
x-z=2
x²+y²+z²-xy-yz-zx
=(1/2)(x²-2xy+y²+y²-2yz+z²+z²-2zx+x²)
=(1/2)[(x-y)²+(y-z)²+(x-z)²]
=(1/2)(1²+1²+2²)
=3