This problem was in my calculus exercise, yet I don't understand why:
Solve the equation :
(Show there are not other solutions to the ones you found)
Now, solving it regularly using simple algebra got me into an eighth-degree polynomial, which reminded my my teachers have just told us there are proofs for why there are no 'formulas' for solving polynomial equations higher than 5.
Anyway, how can I solve this problem using calculus tools? I thought of doing the following thing:
We know that , therefore:
Let the first expression be , ane the second expression be . Therefore:
but how do I find it ?