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- March 5th 2011, 02:15 PMAlex2103Simplify this expression...
- March 5th 2011, 03:33 PMtopsquark
- March 5th 2011, 03:55 PMSoroban
Hello, Alex2103!

Quote:

A binomial of the form makes me suspect

. . that the problem involves the Golden Mean: .

. . .

Therefore:

. .

. .

Iyour solution, Dan!*love*

- March 5th 2011, 04:07 PMtopsquark
- March 6th 2011, 04:51 AMAlex2103
Thanks for help!(Happy)

- March 6th 2011, 12:05 PMHallsofIvy
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 .