已知x/b+c-a=y/c+a-b=z/a+b-c,求(b-c)x+(c-a)y+(a-b)z的值.
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![已知x/b+c-a=y/c+a-b=z/a+b-c,求(b-c)x+(c-a)y+(a-b)z的值.](/uploads/image/z/14233970-2-0.jpg?t=%E5%B7%B2%E7%9F%A5x%2Fb%2Bc-a%3Dy%2Fc%2Ba-b%3Dz%2Fa%2Bb-c%2C%E6%B1%82%28b-c%29x%2B%28c-a%29y%2B%28a-b%29z%E7%9A%84%E5%80%BC.)
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已知x/b+c-a=y/c+a-b=z/a+b-c,求(b-c)x+(c-a)y+(a-b)z的值.
已知x/b+c-a=y/c+a-b=z/a+b-c,求(b-c)x+(c-a)y+(a-b)z的值.
已知x/b+c-a=y/c+a-b=z/a+b-c,求(b-c)x+(c-a)y+(a-b)z的值.
设:x/b+c-a=y/c+a-b=z/a+b-c=k
x=k(b+c-a)
y=k(c+a-b)
z=k(a+b-c)
三式相加得:x+y+z=k(a+b+c)
(b-c)x+(c-a)y+(a-b)z
=k[(b-c)(b+c-a)+(c-a)(c+a-b)+(a-b)(a+b-c)]
=0