Problem: If aξ =b,a3βb3=19x3 and aβb=x, which of the following conclusions is correct?
Answer Choices:
A. a=3x
B. a=3x or a=β2x
C. a=β3x or a=2x
D. a=3x or a=2x
E. a=2x
Solution:
If aξ =b,a3βb3=19x3 and aβb=x, then
a3βb3=(aβb)(a2+ab+b2)=x(a2+ab+b2)=19x3
Dividing by x and substituting b=aβx into the last equality above, we obtain
18x2+3axβ3a2β=0β3(aβ3x)(a+2x)β=0β
So a=3x or a=β2x.