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polynomial of 7th order, some structure
hi, I have an equation i have been trying to solve, but no amount of Solve, Reduce or ToRadical seems to produce an answer. x(1+x^2)^3 == a x^4 +b x^3 +...+e I know that it has one or three real roots, depending on combinations of coefficients, with only one root at x>0. That is the one that I want, the root that is > 0. Does anyone have any ideas what I can do? I can plot the Root results, and I can see that it is usually the same one root from the list, for most coefficient combinations. Any way i can get the formula without plugging in the values?