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This question already has an answer here:

Show that for all positive x $\in$ $\mathbb{R}$ the inequality $x+\dfrac {1} {x}\geq 2$ holds. Can you give me a hint?

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merged by Daniel Fischer Nov 12 '15 at 16:04

This question was merged with How to prove this inequality $ x + \frac{1}{x} \geq 2 $ because it is an exact duplicate of that question.

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