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# Irrational to the Fraction

Let $$a$$ be an irrational number and let $$n$$ be an integer greater than 1. Prove that

$$(a + \sqrt{a^2 - 1})^{\frac {1}{n}} + (a - \sqrt{a^2 - 1})^{\frac {1}{n}}$$

is an irrational number.

Note by Sharky Kesa
3 years, 8 months ago

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$$x^{2}-2ax+1$$.

With roots as:

$$a+ \sqrt{a^{2}-1}$$ & $$a- \sqrt{a^{2}-1}$$

And then use this and try to get the expression above...

- 3 years, 8 months ago