Problem: If aî€ =b,a3−b3=19x3 and a−b=x, which of the following conclusions is correct?
Answer Choices:
A. a=3x
B. a=3x or a=−2x
C. a=−3x or a=2x
D. a=3x or a=2x
E. a=2x
Solution:
If aî€ =b,a3−b3=19x3 and a−b=x, then
a3−b3=(a−b)(a2+ab+b2)=x(a2+ab+b2)=19x3
Dividing by x and substituting b=a−x into the last equality above, we obtain
18x2+3ax−3a2​=0−3(a−3x)(a+2x)​=0​
So a=3x or a=−2x.