por GehSillva7 » Qui Fev 25, 2016 12:55
por adauto martins » Dom Fev 28, 2016 13:38
![a+b\sqrt[]{p}](/latexrender/pictures/99f8728343f5210cbbcb8401d4dd6adf.png "a+b\sqrt[]{p}")
,onde a,b,p
,p primo}...bom,um corpo é um espaço vetorial de dimensao nula,entao temows aquelas 8 propriedades a ser verificadas,farei algumas,tdbem...![0\in Q, pois 0+x=(0+0\sqrt[]{p})+(a+b\sqrt[]{p})=(0+a)+(0+b)\sqrt[]{p}=a+b\sqrt[]{p}=x](/latexrender/pictures/a82f8aa2d2ad3922213cb5b75e3fc31a.png "0\in Q, pois 0+x=(0+0\sqrt[]{p})+(a+b\sqrt[]{p})=(0+a)+(0+b)\sqrt[]{p}=a+b\sqrt[]{p}=x")
...![1\in Q,pois...1.x=(1+0\sqrt[]{p}).(a+b\sqrt[]{p})=(1.a+p.0)+(1.b+0.p.b)\sqrt[]{p}=a+b\sqrt[]{p}=x](/latexrender/pictures/bc2a4ec8df011955d665fbe042c2c6d8.png "1\in Q,pois...1.x=(1+0\sqrt[]{p}).(a+b\sqrt[]{p})=(1.a+p.0)+(1.b+0.p.b)\sqrt[]{p}=a+b\sqrt[]{p}=x")
...
,de fato...![x.{x}^{-1}=(a+b\sqrt[]{p}).(1/(a+b\sqrt[]{p})=(a+b\sqrt[]{p}).(a-b\sqrt[]{p})/({a}^{2}-p.{b}^{2})={a}^{2}-p.{b}^{2}/({a}^{2}-p.{b}^{2})=1](/latexrender/pictures/a499118cc6998a170a2253c2069e29d3.png "x.{x}^{-1}=(a+b\sqrt[]{p}).(1/(a+b\sqrt[]{p})=(a+b\sqrt[]{p}).(a-b\sqrt[]{p})/({a}^{2}-p.{b}^{2})={a}^{2}-p.{b}^{2}/({a}^{2}-p.{b}^{2})=1")
...as outras 5 sao mais facieis...verifique-as...
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![\frac{\sqrt[]{\sqrt[4]{8}+\sqrt[]{\sqrt[]{2}-1}}-\sqrt[]{\sqrt[4]{8}-\sqrt[]{\sqrt[]{2}-1}}}{\sqrt[]{\sqrt[4]{8}-\sqrt[]{\sqrt[]{2}+1}}}](/latexrender/pictures/981987c7bcdf9f8f498ca4605785636a.png "\frac{\sqrt[]{\sqrt[4]{8}+\sqrt[]{\sqrt[]{2}-1}}-\sqrt[]{\sqrt[4]{8}-\sqrt[]{\sqrt[]{2}-1}}}{\sqrt[]{\sqrt[4]{8}-\sqrt[]{\sqrt[]{2}+1}}}")
![\sqrt[]{2}](/latexrender/pictures/f21662d1cabab6e8b273a4b6f1cd663a.png "\sqrt[]{2}")
(dica : igualar a expressão a 
e elevar ao quadrado os dois lados)