Problem: If b+ca+bβ=d+ac+dβ, then:
Answer Choices:
A. a must equal c
B. a+b+c+d must equal zero
C. either a=c or a+b+c+d=0, or both
D. a+b+c+dξ =0 if a=c
E. a(b+c+d)=c(a+b+d)
Solution:
Since b+ca+bβ=d+ac+dβ, then c+da+bβ=d+ab+cβ and c+da+bβ+1=d+ab+cβ+1
β΄c+da+b+c+dβ=a+da+b+c+dβ. If a+b+c+dξ =0, then a=c.
If a+b+c+d=0, then a may or may not equal c, so that the correct choice is (C).