# Find all the real values of a?

• May 23rd 2009, 10:09 PM
fardeen_gen
Find all the real values of a?
Find all the real values of $a$ for which $a^3 + a^2|a + x| + |a^2x + 1| = 1$ has at least 4 integral solutions in $x$.
• May 24th 2009, 12:24 AM
CaptainBlack
Quote:

Originally Posted by fardeen_gen
Find all the real values of $a$ for which $a^3 + a^2|a + x| + |a^2x + 1| = 1$ has at least 4 integral solutions in $x$.

Split this into four cases:

$a+x \ge 0,\ a^2x+1 \ge 0$

$a+x <0,\ a^2x+1 \ge 0$

$a+x \ge 0, \ a^2x+1 <0$

$a+x < 0, \ a^2x+1<0$

to give four problems but without absolute values in the equations.

CB