Re:[obm-l] racionalizar

De:

owner-obm-l@mat.puc-rio.br

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.