Question

對于非零實數(shù)x，y，z，設(shè)

x+y-z

z

=

x-y+z

y

=

-x+y+z

x

=t，那么t的值（　�。�

• A、必定是1
• B、可以是±1
• C、可以是1或-2
• D、將隨x，y，z而變化

Answer 1

分析：此題應(yīng)考慮兩種情況：當(dāng)x+y+z≠0時，根據(jù)等比性質(zhì)求解；當(dāng)x+y+z=0時，從中導(dǎo)出x+y=-z，代入即可求解．

解答：解：當(dāng)x+y+z≠0時，則有t=

x+y+z

x+y+z

=1；
當(dāng)x+y+z=0時，則有x+y=-z，即t=

-2z

z

=-2．
故選C．

點評：此題主要是等比性質(zhì)的運用：若

a

b

=

c

d

=…=

m

n

=k，則

a+c+…+m

b+d+…+n

=k（b+d+…+n≠0）．