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Re: [obm-l] Desigualdade
- To: obm-l@xxxxxxxxxxxxxx
- Subject: Re: [obm-l] Desigualdade
- From: "Marcelo Salhab Brogliato" <msbrogli@xxxxxxxxx>
- Date: Mon, 20 Aug 2007 22:04:18 -0300
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Olá Bruna,
acredito que seja para a, b reais nao-negativos..dai vc pode usar algumas estrategias...
1) desigualdade das medias.. media aritmetica >= media geometricaficaria: (a/b + b/a)/2 >= sqrt(a/b * b/a) = 1
2) sabemos que (sqrt(a/b) - sqrt(b/a))^2 >= 0entao: a/b - 2sqrt(a/b)sqrt(b/a) + b/a >= 0a/b + b/a >= 2 [bom, esta eh a demonstracao da desigualdade das mediaspara o caso de 2 termos]
abracos,Salhab
On 8/20/07, Bruna Carvalho <bruna.carvalho.pink@gmail.com> wrote:> Demonstrar a seguinte desilgualdade> a/b + b/a ≥ 2, para todo a e b real não nulo.>> --> Bjos,> Bruna
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