Mathematics: Prove that if x is irrational, then 1/x is irrational

Prove that if x is irrational, then 1/x is irrational

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sanago4785

09.01.2022

Proof by contradiction.

Let assume that when is an irrational number, then $\dfrac{1}{x}$ is a rational number.

If $\dfrac{1}{x}$ is a rational number, then it can be expressed as a fraction $\dfrac{a}{b}$ where $a,b\in\mathbb{Z}$ .

$\dfrac{1}{x}=\dfrac{a}{b} \Rightarrow x=\dfrac{b}{a}$

Since $a,b\in\mathbb{Z}$ , the number $x=\dfrac{b}{a}$ is also a rational number. But this contardicts our initial assumption that is an irrational number. Therefore $\dfrac{1}{x}$ must be an irrational number.

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Ответ:

mary9590

10.11.2020

Mathematics

Hii! I got y = 18* sin(0.4205*x+0.7297). I hope its right. And hoped I helped.

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Prove that if x is irrational, then 1/x is irrational

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