Message Boards Message Boards

0
|
3764 Views
|
1 Reply
|
0 Total Likes
View groups...
Share
Share this post:

Finding the range of positive or negative values

Posted 9 years ago

I have the following expression for $\sigma$ $$\sigma = \lambda -15 (\rho_a^2 + \rho_b^2) + \sqrt{9(\rho_a^4 + \rho_b^4) + \gamma^2 - 48 \gamma \rho_a \rho_b + 558 \rho_a^2 \rho_b^2} $$ And I wish to find the ranges of $\lambda$ for which $\sigma$ is negative. The forms of $\rho_a$ and $\rho_b$ are the following $$\rho_a = \sqrt{\frac{\lambda + \sqrt{\lambda^2 - \gamma^2}}{6}} \\\rho_b = \sqrt{\frac{\lambda - \sqrt{\lambda^2 - \gamma^2}}{6}}$$ When I use $Solve[\sigma < 0 , \lambda]$ I get an error message saying that I should use $Reduce$ for complete solution information, but I don't understand how to do it.

I attach here the notebook that I use for this problem.

Attachments:
POSTED BY: Omer Tzuk
Posted 9 years ago

Got it, I was confused on how to use $Reduce$, but I figured it out..

POSTED BY: Omer Tzuk
Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Reply Preview
Attachments
Remove
or Discard

Group Abstract Group Abstract