若实数a、b、c、d满足ab=bc=cd=da,则ab+bc+cd+daa2+b2+c2+d2的值是(  )A.1或0B.-1或0C.1或-2D

2025-06-20 08:42:07
推荐回答(1个)
回答1:

a
b
b
c
c
d
d
a
=k,
则b2=ac,c2=bd,d2=ac=b2,a2=bd=c2
a
b
=k得,a=bk,
d
a
=k得,d=ak=bk2
c
d
=k得,c=dk=bk3
再由
b
c
=k得,
b
bk3
=k,
即:k4=1,
k=±1.
当k=1时,原式=1;
当k=-1时,原式=-1;
故选D.