1

I am trying to solve for a2 in the equation below:

(-((ρ σ1 σ2)/(a2 a3)) + σ2^2)^2 
 > (σ2^2 (-2 a3 ρ σ1 σ2 + a2 (σ1^2 + a3^2 σ2^2)))/(a2^2 a3^3)

I would like to arrange this expression in terms of a2 or a3 if possible.

So far I've tried using Reduce, together with some assumptions intended to produce a 'nice' solution:

Reduce[(-((ρ σ1 σ2)/(a2 a3)) + σ2^2)^2 > 
 (σ2^2 (-2 a3 ρ σ1 σ2 + a2 (σ1^2 + a3^2 σ2^2)))/(a2^2 a3^3) && 
 σ1 > 0 && \[Sigma]2 > 0 && -1 <= ρ <= 1, {a2}]

But Mathematica returns a large output which I don't fully understand; I don't know which solution to take or leave.

LLlAMnYP
  • 11,486
  • 26
  • 65
user3331868
  • 11
  • 2
  • If no further assumptions are allowed you have to realize that the full output is most likely a correct solution, or if if another assumptions you have in mind you should specify them in the input. With appropriate assumptions on a3 or a2 there is still a some space to find a simpler expression. Perhaps you'll find convenient the Backsubstitution -> True option. You should probably read also e.g. How do I work with Root objects? – Artes Nov 03 '14 at 16:40
  • Reduce[.., {a2, a3, ρ, σ1, σ2}] yields a cylindrical decomposition of the inequality in which inequalities for σ1 are given in terms of σ2, for ρ in terms of σ1 and σ2, for a3 in terms of ρ, σ1, σ2 etc. The inequalities for each variable are divided into cases with Or; the inequalities for one variable is connected to the next by And. The whole can be represented in a nice tree structure, but since And is Flat, the expression does not usually have this structure. – Michael E2 Nov 03 '14 at 17:56
  • ow than you so much for this – user3331868 Dec 07 '14 at 11:36

0 Answers0