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# Random Inequality

If $$x$$ and $$y$$ are distinct positive reals, prove the inequality

$\large \sqrt{xy} < \frac{y-x}{\ln(y) - \ln(x)} < \frac{x+y}2.$

Note by Karan Jain
10 months, 3 weeks ago

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Let $$\large y=\displaystyle\lim _{ h\rightarrow 0 }{ x+h }$$. · 8 months, 4 weeks ago