Question

若

2b+2c

a

=

2a+2c

b

=

2a+2b

c

=k，則k的值為（　�。�

• A、4
• B、0
• C、-2或0
• D、4或-2

Answer 1

分析：先將

2b+2c

a

=

2a+2c

b

=

2a+2b

c

=k變形為若

a+b

c

=

b+c

a

=

c+a

b

=

1

2

k，再根據(jù)等比性質(zhì)計算，注意條件的限制．

解答：解：∵

2b+2c

a

=

2a+2c

b

=

2a+2b

c

=k，
∴

b+c

a

=

a+c

b

=

a+b

c

=

1

2

k，
分情況進行：當(dāng)a+b+c≠0時，根據(jù)等比性質(zhì)，得

1

2

k=

2c+2a+2b

c+a+b

=2，則k=4；
當(dāng)a+b+c=0時，則a+b=-c，

1

2

k=-1，則k=-2．
故選D．

點評：熟悉等比性質(zhì)：若

a

b

=

c

d

=…=

m

n

=k，則

a+c+…+m

b+d+…+n

=k，（b+d+…+n≠0）．特別注意條件的限制．