System of equations with Mathematica

AI Thread Summary
The discussion centers around the challenges of solving a complex system of equations using Mathematica. The user expresses dissatisfaction with Maple and seeks assistance with a system that includes a quartic equation and an inequality, noting that Mathematica may struggle due to the presence of five unknowns but only one equation and one inequality. It is suggested that while the equation can be rearranged to express one variable in terms of others, the solutions will be complicated and lengthy. The conversation highlights the limitations of Mathematica in handling such systems effectively. Ultimately, the complexity of the expressions and the number of variables make finding a straightforward solution difficult.
Siron
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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!
 
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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.
 
Ackbach said:
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 ...
 
Siron said:
$$\left \{ \begin{array}{ll} 16x^4-40ax^3+(15a^2+24b)x^2-18abx+3b^2 = 0 \\ 4x^4+5a s \sqrt{v} x^2 - 8 s \sqrt{v} x^3 - b s \sqrt{v} x > 0 \end{array} \right.$$
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.
 
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