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[obm-l] Provar que k + raiz(k^2 +a ) eh irracional

To: <obm-l@xxxxxxxxxxxxxx>
Subject: [obm-l] Provar que k + raiz(k^2 +a ) eh irracional
From: "Artur Costa Steiner" <artur.steiner@xxxxxxxxxx>
Date: Thu, 2 Aug 2007 14:37:05 -0300
In-Reply-To: <46B208DA.4A1BB467@trieste.fapesp.br>
Reply-To: obm-l@xxxxxxxxxxxxxx
Sender: owner-obm-l@xxxxxxxxxxxxxx
thread-index: AcfVJeTTSx4enSeuSqaAlhJOgzUi/QAAz0Rw
Thread-Topic: [obm-l] f(f(x)) = x^2 - 1996

Este problema parece complicado, mas tendo-se um "clique" apresenta uma solucao simples, Achei interessante.

Seja a um numero racional. Mostre que, se k for irracional e k^2 + a >=0, então k + raiz(k^2 + a) eh irracional.

Artur

Follow-Ups:
- Re: [obm-l] Provar que k + raiz(k^2 +a ) eh irracional
  - From: saulo nilson
- Re: [obm-l] Provar que k + raiz(k^2 +a ) eh irracional
  - From: Demetrio Freitas

References:
- Re: [obm-l] f(f(x)) = x^2 - 1996
  - From: ralonso

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