I have a problem: I want to solve this equation:
x^3+(3c-1)(x^2)-4cx-4(c^2)=0 with respect to x.
It has to have a real solution because it is continuous
in x. c is a positive parameter.
If i solve it numerically, plugging numbers for c, then it is fine. But I would like an analytical solution: in this case i get only one solution which should give me a real value for x (the other two are imaginary) but
it has a square root with all negative members (all terms with c, which is positive, with a sign - in front of it, so immaginary). How is that possible? What procedure does mathematica use to solve cubic expression?
How can I express the expression in a nicer way to get rid of these negative terms? My feeling is that the programm is not able to simplify the expression for the solution.
Could you please help me? if I write the expression I find in the paper I am writing, noone will believe it is real!
And even more funny, if I plug number into the solution I find for x, it comes the same number as I plug numbers directly into the function I want to solve, except for the last part which is an imaginary number which shoult tend to zero.
What is going on?