A binomial of the form makes me suspect
. . that the problem involves the Golden Mean: .
. . .
I love your solution, Dan!
Thanks for help!(Happy)
Heres' yet another way to do that. Cardano's formula for the reduced cubic equation says that a solution to is of the form .
Looks familiar, doesn't it? That is precisely the same as with and .
From , n= 4 and then so that , , and .
That means that this number is a real root of or . It is easy to see that . Since the discriminant of is the only real root of that equation is 1 so we must have .