# Math Help - nice inequality

hi ,

2. ## Re: nice inequality

Originally Posted by abualabed
hi ,

Here a graphical solution.

3. ## Re: nice inequality

Abualabed

since x^2=|x|^2 if you substitute |x| with another variable like t you will get the qubic inequality t^3-2t^2-4t+3<0

Consider the qubic equation t^3-2t^2-4t+3 =0 and verify that t=3 is a solution . thus factorize the qubic polynomial using Horner's scheme or full division by (t-3) and find t^3-2t^2-4t+3 =(t-3)(t^2+t-1) .
then solve the equation (t-3)(t^2+t-1) =0 to find the roots it is easy..
then go back to |x|=t and do the rest ...it is easy.
your final solution is in the attached figure.

4. ## Re: nice inequality

Hi,
Here's a graphical solution as suggested by Plato: