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I need some help with the following problem:

Show that for any pair $(a,b)$ of positive integers, $\dfrac{a+2b}{a+b} < \sqrt{2} < \dfrac{a}{b}$.

I tried squaring both sides of the inequality, but I was not able to solve it.

quid
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yumiko
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    This is false, take $ a = b = 1 $, for instance. – Ege Erdil Sep 20 '16 at 16:53
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    Okay, re:downvote(s). The "duplicate" as referred above: "Let $a$ and $b$ be positive integers. Show that $\sqrt{2}$ always lies between $\dfrac{a}{b}$ and $\dfrac{a+2b}{a+b}$. Please give the easy solution as possible" received three upvotes. This question is superior to that question (just quoted) in terms of asking and not telling.. So why the downvotes here, but not there? – amWhy Sep 20 '16 at 17:43
  • Try looking at $$\dfrac{a+2b}{a+b} > \sqrt{2} > \dfrac{a}{b}$$ – amWhy Sep 20 '16 at 17:48
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    @yumiko this is a case which reveals the non-uniform standards in accepting a question, and rejecting it. As you see in the third comment, voting is decidedly arbitrary at this site. So don't take the inconsistent standards at this site personally! – amWhy Sep 20 '16 at 17:50

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