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| − | = | + | = Problem 5 = |
| + | Clearly <math>\mathbb{Q}(\alpha)\subset \mathbb{Q}(2^{\frac{1}{3}})</math>. But also, | ||
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| + | <math>2\alpha - \alpha = 16-17 \cdot 2^{\frac{1}{3}}</math> | ||
| + | So <math>\mathbb{Q}(2^{\frac{1}{3}}) = \mathbb{Q}(\alpha)</math>. | ||
| − | + | Thus <math>3=|\mathbb{Q}(2^{\frac{1}{3}}):\mathbb{Q}| = |\mathbb{Q}(\alpha):\mathbb{Q}|</math>. | |
| + | <br> | ||
| + | [[NinjaSharksSet5|Back to NinjaSharksSet5]] | ||
| − | + | [[Category:NinjaSharksSet5]] | |
| − | [[ | + | |
Revision as of 04:10, 3 July 2013
Problem 5
Clearly $ \mathbb{Q}(\alpha)\subset \mathbb{Q}(2^{\frac{1}{3}}) $. But also,
$ 2\alpha - \alpha = 16-17 \cdot 2^{\frac{1}{3}} $
So $ \mathbb{Q}(2^{\frac{1}{3}}) = \mathbb{Q}(\alpha) $.
Thus $ 3=|\mathbb{Q}(2^{\frac{1}{3}}):\mathbb{Q}| = |\mathbb{Q}(\alpha):\mathbb{Q}| $.
