# Show that for all positive x $\in$ $\mathbb{R}$ the inequality $x+\frac {1} {x}\geq 2$ holds. (Hint?) [duplicate]

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