 |
 |
Hi All Well done Ignacio, I made assumptions about Q that I ought not to have, Cheers Terence Terence Etchells BSc, MSc, MIMA, CMath Senior Lecturer in Mathematics Liverpool John Moores University Liverpool,UK -----Original Message----- From: DERIVE computer algebra system [mailto:[log in to unmask]] On Behalf Of Ignacio Larrosa Cañestro Sent: 07 November 2003 11:22 To: [log in to unmask] Subject: Re: Simple question about rational demoninators? (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) [log in to unmask]