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[SPAM] [obm-l] Res: [obm-l] Provar que é quadrado perfeito



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Ol=E1 Arthur=0AFa=E7a assim: a=3D 1+sqrt(2) =3D=3D> a^2 =3D 3+sqrt(8) e 1/a=
^2 =3D 3-sqrt(8) de forma que temos=0Aa^(2n) - 1/a^(2n) - 2 =3D (a^n - 1/a^=
n)^2. Resta somente provar que a^n - 1/a^n eh inteiro. Basta  racionalizar =
e fazer a expansao binomial.=0A[]'s=0A     Danilo.=0A=0A=0A----- Mensagem o=
riginal ----=0ADe: Artur Costa Steiner <artur.steiner@xxxxxxxxxx>=0APara: "=
obm-l@xxxxxxxxxxxxxx" <obm-l@xxxxxxxxxxxxxx>=0AEnviadas: Ter=E7a-feira, 19 =
de Fevereiro de 2008 15:34:30=0AAssunto: [obm-l] Provar que =E9 quadrado pe=
rfeito=0A=0A=0AGostaria que algu=E9m desse alguma sugest=E3o para isto:=0A =
=0AMostre que, para todo n =EDmpar positivo, (3 + raiz(8))^n + (3 - raiz(8)=
)^n  -  2 eh um quadrado perfeito.=0A =0AAbracos=0AArtur=0A=0A=0A      Abra=
 sua conta no Yahoo! Mail, o =FAnico sem limite de espa=E7o para armazename=
nto!=0Ahttp://br.mail.yahoo.com/
--0-1342267679-1203822519=:99639
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Content-Transfer-Encoding: quoted-printable

<html><head><style type=3D"text/css"><!-- DIV {margin:0px;} --></style></he=
ad><body><div style=3D"font-family:times new roman, new york, times, serif;=
font-size:12pt"><DIV style=3D"FONT-SIZE: 12pt; FONT-FAMILY: times new roman=
, new york, times, serif">Ol=E1 Arthur</DIV>=0A<DIV style=3D"FONT-SIZE: 12p=
t; FONT-FAMILY: times new roman, new york, times, serif">Fa=E7a assim: a=3D=
 1+sqrt(2) =3D=3D&gt; a^2 =3D 3+sqrt(8) e 1/a^2 =3D 3-sqrt(8) de forma que =
temos</DIV>=0A<DIV style=3D"FONT-SIZE: 12pt; FONT-FAMILY: times new roman, =
new york, times, serif">a^(2n) - 1/a^(2n) - 2 =3D (a^n - 1/a^n)^2.&nbsp;Res=
ta somente provar que a^n - 1/a^n eh inteiro.&nbsp;Basta&nbsp; racionalizar=
 e&nbsp;fazer a expansao binomial.</DIV>=0A<DIV style=3D"FONT-SIZE: 12pt; F=
ONT-FAMILY: times new roman, new york, times, serif">[]'s</DIV>=0A<DIV styl=
e=3D"FONT-SIZE: 12pt; FONT-FAMILY: times new roman, new york, times, serif"=
>&nbsp;&nbsp;&nbsp;&nbsp; Danilo.<BR><BR></DIV>=0A<DIV style=3D"FONT-SIZE: =
12pt; FONT-FAMILY: times new roman, new york, times, serif">----- Mensagem =
original ----<BR>De: Artur Costa Steiner &lt;artur.steiner@xxxxxxxxxx&gt;<B=
R>Para: "obm-l@xxxxxxxxxxxxxx" &lt;obm-l@xxxxxxxxxxxxxx&gt;<BR>Enviadas: Te=
r=E7a-feira, 19 de Fevereiro de 2008 15:34:30<BR>Assunto: [obm-l] Provar qu=
e =E9 quadrado perfeito<BR><BR>=0A<DIV><FONT face=3DArial color=3D#0000ff s=
ize=3D2><SPAN class=3D983123218-19022008>Gostaria que algu=E9m desse alguma=
 sugest=E3o para isto:</SPAN></FONT></DIV>=0A<DIV><FONT face=3DArial color=
=3D#0000ff size=3D2><SPAN class=3D983123218-19022008></SPAN></FONT>&nbsp;</=
DIV>=0A<DIV><FONT face=3DArial color=3D#0000ff size=3D2><SPAN class=3D98312=
3218-19022008>Mostre que, para todo n =EDmpar positivo, (3 + raiz(8))^n + (=
3 - raiz(8))^n&nbsp; -&nbsp; 2 eh um quadrado perfeito.</SPAN></FONT></DIV>=
=0A<DIV><FONT face=3DArial color=3D#0000ff size=3D2><SPAN class=3D983123218=
-19022008></SPAN></FONT>&nbsp;</DIV>=0A<DIV><FONT face=3DArial color=3D#000=
0ff size=3D2><SPAN class=3D983123218-19022008>Abracos</SPAN></FONT></DIV>=
=0A<DIV><FONT face=3DArial color=3D#0000ff size=3D2><SPAN class=3D983123218=
-19022008>Artur</SPAN></FONT></DIV></DIV>=0A<DIV style=3D"FONT-SIZE: 12pt; =
FONT-FAMILY: times new roman, new york, times, serif"><BR></DIV></div><br>=
=0A=0A=0A      <hr size=3D1>Abra sua conta no <a href=3D"http://br.rd.yahoo=
.com/mail/taglines/mail/*http://br.mail.yahoo.com/";>Yahoo! Mail</a>, o =FAn=
ico sem limite de espa=E7o para armazenamento! =0A</body></html>
--0-1342267679-1203822519=:99639--
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