Question

Solve for x in terms of a, the inequality |x²-3ax+2a²| < |x²+3ax-a²|, where x includes all real numbers, a≠0

Answer 1

if this is on homework, don't do it

if this a test question, don't do it either

XDD

Answer 2

you'll go crazy trying to solve it

Answer 3

Either this will help\[
|a|<|b| \implies |a|^2<|b|^2\implies a^2<b^2
\]Or you will have to consider the 4 cases where either side is positive or negative.

Answer 4

Also \[
|x^2-3ax+2a^2 |= |(x^2+3ax-a^2)+(6ax-3a^2)|
\]