System of equations with Mathematica

[Siron]

Hello!

I'm currently working with Maple but I do not really like the program. Is there someone with Mathematica who can run this system?

$$\left \{ \begin{array}{ll} 16x^4-40ax^3+(15a^2+24b)x^2-18abx+3b^2 = 0 \\ 4x^4+5a s \sqrt{v} x^2 - 8 s \sqrt{v} x^3 - b s \sqrt{v} x > 0 \end{array} \right.$$

If it would help $a<0$ and $s<0$.

Thanks!

 

[Ackbach]

Hmm. Mathematica is not going to be able to solve your system fully, because you have five unknowns, but only one equation and one inequality. You can find $x$ in terms of $a$ and $b$, but that's a quartic, which will be horrendous. It'll take pages just to write down the solution. As for the inequality, I'm not sure Mathematica could glean much of anything from that.

 

[Siron]

Hmm. Mathematica is not going to be able to solve your system fully, because you have five unknowns, but only one equation and one inequality. You can find $x$ in terms of $a$ and $b$, but that's a quartic, which will be horrendous. It'll take pages just to write down the solution. As for the inequality, I'm not sure Mathematica could glean much of anything from that.

Thanks Ackbach! I knew I could expecting something like this. These ugly expressions keep coming ...

 

[Wilmer]

$$\left \{ \begin{array}{ll} 16x^4-40ax^3+(15a^2+24b)x^2-18abx+3b^2 = 0 \\ 4x^4+5a s \sqrt{v} x^2 - 8 s \sqrt{v} x^3 - b s \sqrt{v} x > 0 \end{array} \right.$$

With all those variables and 1 equation only, what is the problem statement?

The equation can be rearranged in terms of b (as example):

b = [-u +- SQRT(u^2 - 12v)] / 6
where:
u = 24x^2 - 18ax
v = 16x^4 - 40ax^3 + 15ax^2

So if x and a are givens, then you can solve for b.