De:[EMAIL PROTECTED]
Para:obm-l@mat.puc-rio.br
Cópia:
Data:Wed, 25 Apr 2007 12:12:02 +0000
Assunto:[obm-l] racionalizar
> Sauda,c~oes,
>
> Como se racionaliza X/Y, com
>
> X = a^{15} - 1 e
>
> Y = a^{3/16} + a(a^{1/8}) + a^2(a^{1/16}) + a^3 ?
>
Y = (a^(1/4) - a^4)/(a^(1/16) - a) ==>
X/Y = (a^15 - 1)*(a^(1/16) - a)/(a^(1/4) - a^4)
Mas:
(a^(1/4) - a^4)*(a^(3/4) + a^4*a^(1/2) + a^8*a^(1/4) + a^12) =
a - a^16
Logo:
X/Y =
(a^15 - 1)*(a^(1/16) - a)*(a^(3/4) + a^(9/4) + a^(33/4) + a^12)/
(a - a^16) ==>
X/Y = (a - a^(1/16))*(a^(3/4) + a^(9/4) + a^(33/4) + a^12)/a
[]s,
Claudio.
