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Edward Hughes
Frequent poster

Post Number: 174
 Posted on Saturday, 22 October, 2011 - 02:48 pm:

Could someone point out where my logic is wrong in the following?

$Q(\sqrt{2} + \sqrt{3})$ has subextensions $Q(\sqrt{3}), Q(\sqrt{2}), Q(\sqrt{6})$ and minimal polynomial $P(X) = X^4 - 10X^2 + 1$. It's easy to factorise P over the first two of the extensions above, but I should be able to over $Q(\sqrt{6})$ as well, right? Is there a trivial factorisation I'm missing? Or am I wrong in thinking that $Q(\sqrt{6})$ is a subextension?

lebesgue
Veteran poster

Post Number: 2429
 Posted on Saturday, 22 October, 2011 - 03:04 pm:

(x2-5-2sqrt(6))(x2-5+2sqrt(6))?
Edward Hughes
Frequent poster

Post Number: 175
 Posted on Sunday, 23 October, 2011 - 01:56 am:

I thought of that myself about 5 minutes after I posted the question - thanks!