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[SPAM] Re: [obm-l] equação
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Hm, eu imaginei outra solução.
Pel desigualdade das médias potenciais, a média de
ordem 7 é maior ou igual à média de ordem 1 (a média
aritmética). Nesse caso, as médias são de sen^2 x e
cos^2 x.
((sen^14 x + cos^14 x)/2)^{1/7}
>= (sen^2 x + cos^2 x)/2 = 1/2
<=> sen^14 x + cos^14 x >= 2(1/2)^7 = 1/64
Isto quer dizer que se sen^14 x + cos^14 x = 1/64
ocorre a igualdade na desigualdade das médias
potenciais, o que só pode ocorrer quando sen^2 x =
cos^2 x.
Eu acho que sai usando a desigualdade de Bernoulli,
mas não consegui uma demonstração agora.
[]'s
Shine
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