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[SPAM] [obm-l] Re: [obm-l] Eq. do 2º Grau de Coef. Inteiros



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Ol=E1
Primeiro =E9 =FAtil usar o seguinte fato: todo inteiro elevado ao =
quadrado deixa resto 0 ou 1 na divis=E3o por 3 ou por 4 (tente provar =
isso...se n=E3o der mande outro email).
Seja ax^2+bx+c com a, b, c inteiros. O discriminante =E9: b^2 - 4ac. =
Suponha por absurdo que b^2 - 4ac =3D 39. Ent=E3o: b^2=3D39+4ac. Veja =
que dividindo os dois lados por 4 temos: (b^2)/4=3D39/4 + ac. Se fosse =
poss=EDvel encontrar inteiros que satisfazem a igualdade, o resto do =
lado direito deveria ser 0 ou 1. Mas 39/4 deixa resto 3. Logo =E9 =
imposs=EDvel encontrar inteiros que satisfazem a igualdade, ou seja, o =
discriminante n=E3o pode ser 39.
Abra=E7os
  ----- Original Message -----=20
  From: Pedro J=FAnior=20
  To: obm-l@xxxxxxxxxxxxxx=20
  Sent: Thursday, February 28, 2008 11:17 PM
  Subject: [obm-l] Eq. do 2=BA Grau de Coef. Inteiros


  Dada uma equa=E7=E3o do 2=BA Grau, com coeficientes inteiros, mostre =
que seu discriminante n=E3o pode ser igual a 39.


  Agrade=E7o desde j=E1...
  Atenciosamente Pedro Jr (Jo=E3o Pessoa)

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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META http-equiv=3DContent-Type content=3D"text/html; =
charset=3Diso-8859-1">
<META content=3D"MSHTML 6.00.2900.3268" name=3DGENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=3D#ffffff>
<DIV><FONT face=3DArial size=3D2>Ol=E1</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>Primeiro =E9 =FAtil usar o seguinte =
fato: todo inteiro=20
elevado ao quadrado deixa resto 0 ou 1 na divis=E3o por 3 ou por 4 =
(tente provar=20
isso...se n=E3o der mande outro email).</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>Seja ax^2+bx+c com a, b, c inteiros. O=20
discriminante =E9: b^2 - 4ac. Suponha por absurdo que b^2 - 4ac =3D 39. =
</FONT><FONT=20
face=3DArial size=3D2>Ent=E3o: b^2=3D39+4ac. </FONT><FONT face=3DArial =
size=3D2>Veja que=20
dividindo os dois lados por 4 temos: (b^2)/4=3D39/4&nbsp;+ ac. =
</FONT><FONT=20
face=3DArial size=3D2>Se fosse poss=EDvel encontrar inteiros que =
satisfazem a=20
igualdade, o resto do lado direito deveria ser 0 ou 1. </FONT><FONT =
face=3DArial=20
size=3D2>Mas 39/4 deixa resto 3. Logo =E9 imposs=EDvel encontrar =
inteiros que=20
satisfazem a igualdade, ou seja, o discriminante n=E3o pode ser =
39.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>Abra=E7os</FONT></DIV>
<BLOCKQUOTE=20
style=3D"PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; =
BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
  <DIV style=3D"FONT: 10pt arial">----- Original Message ----- </DIV>
  <DIV=20
  style=3D"BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: =
black"><B>From:</B>=20
  <A title=3Dpedromatematico06@xxxxxxxxx=20
  href=3D"mailto:pedromatematico06@xxxxxxxxx";>Pedro J=FAnior</A> </DIV>
  <DIV style=3D"FONT: 10pt arial"><B>To:</B> <A =
title=3Dobm-l@xxxxxxxxxxxxxx=20
  href=3D"mailto:obm-l@xxxxxxxxxxxxxx";>obm-l@xxxxxxxxxxxxxx</A> </DIV>
  <DIV style=3D"FONT: 10pt arial"><B>Sent:</B> Thursday, February 28, =
2008 11:17=20
  PM</DIV>
  <DIV style=3D"FONT: 10pt arial"><B>Subject:</B> [obm-l] Eq. do 2=BA =
Grau de Coef.=20
  Inteiros</DIV>
  <DIV><BR></DIV>Dada uma equa=E7=E3o do 2=BA Grau, com coeficientes =
inteiros, mostre=20
  que seu discriminante n=E3o pode ser igual a 39.<BR><BR><BR>Agrade=E7o =
desde=20
  j=E1...<BR>Atenciosamente Pedro Jr (Jo=E3o =
Pessoa)<BR></BLOCKQUOTE></BODY></HTML>

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