Of course,Originally Posted by dan
Substitute,
Thus,
Cube both sides,
Expand and solve for the nasty nontic.
Note, the solutions not necessarily can be expressed in algebraic terms.
If you are happy with approximate solutions one could start garphically.Originally Posted by dan
These two equations represent curves in the x-y plane. Sketch them
and your first approximation to the soution/s will be the point/s of
intersection.
Then they can be refined with an appropriate numerical procedure (say
linearising about the approximate roots, or something like that).
RonL
Not necessarily there is a general method.Originally Posted by dan
Yes, you do expand with binomial theorem then work with polynomial equation.
(Do you not just love it when mathematicians say "I cannot solve the problem but I can show it cannot be solved!")
What do you get if you substitute this back into the original equations?Originally Posted by dan
Is there a x which with this as a value of y solves the equations?
RonL
(when I do this I get no consistent solution for x, but I could be doing the
arithmetic wrongly )