. 已知Z分之X+Y-Z等于Y分之X-Y+Z等于X分之-X+Y+Z,且XYZ≠0,求分式xyz分之

2025-01-08 01:29:37
推荐回答(2个)
回答1:

(x+y-z)/z=(z+x-y)/y=(y+z-x)/x
[x+y]/z-1=[y+z]/x-1=[z+x]/y-1
[x+y]/z=[y+z]/x=[z+x]/y
设[x+y]/z=[y+z]/x=[z+x]/y=k

k[x+y+z]=[(y+z)/x]*x+[(z+x)/y]*y+[(x+y/z]*z=2[x+y+z]

k=2

(x+y)(y+z)(z+x)/xyz
=(x+y)/z*(y+z)/x*(z+x)/y=2*2*2=8

回答2:

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