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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?

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

Many thanks in advance
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!

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