(Friday, November 07, 2003 12:11 PM)
Terence Etchells <[log in to unmask]> escribió:
> Hi All
>
> I believe there are no flaws in the proof (let me know if there are
> any) below that 1/(1-5^(1/3)) cannot be transformed into an
> expression with a rational denominator. Does anyone have a simpler
> proof? I'm sure Johann Wiesenbauer will have one?
>
We have that a^3 - b^3 = (a - b)(a^2 + ab +b^2). Then let a = 1 and b =
5^(1/3), and multiply and divide for )(a^2 + ab +b^2).
You get,
1/(1-5^(1/3)) = - (1 + 5^(1/3) + 5^(2/3))/4
Saludos,
Ignacio Larrosa Cañestro
A Coruña (España)
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