已知:x=2a-b-c,y=2b-c-a,z=2c-a-b,试简化:(b-c)x+(c-a)y+(a-b)z
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/09 07:50:30
已知:x=2a-b-c,y=2b-c-a,z=2c-a-b,试简化:(b-c)x+(c-a)y+(a-b)z
(b-c)x+(c-a)y+(a-b)z
=bx-cx+cy-ay+az-bz
=az-ay+bx-bz+cy-cx
=a(z-y)+b(x-z)+c(y-x)
z-y=2c-a-b-2b+c+a=3c-3b
x-z=2a-b-c-2c+a+b=3a-3c
y-z=2b-c-a-2a+b+c=3b-3a
a(z-y)+b(x-z)+c(y-x)
=a(3c-3b)+b(3a-3c)+c(3b-3a)
=3ac-3ab+3ab-3bc+3bc-3ac
=3ac-3ac+3ab-3ab+3bc-3bc
=0
=bx-cx+cy-ay+az-bz
=az-ay+bx-bz+cy-cx
=a(z-y)+b(x-z)+c(y-x)
z-y=2c-a-b-2b+c+a=3c-3b
x-z=2a-b-c-2c+a+b=3a-3c
y-z=2b-c-a-2a+b+c=3b-3a
a(z-y)+b(x-z)+c(y-x)
=a(3c-3b)+b(3a-3c)+c(3b-3a)
=3ac-3ab+3ab-3bc+3bc-3ac
=3ac-3ac+3ab-3ab+3bc-3bc
=0
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