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# super hard Cauchy-Schwarz problem

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Let $$x$$ and $$y$$ be positive real numbers such that $$\frac{1}{x + 2} + \frac{1}{y + 2} = \frac{1}{3}.$$
Find the minimum value of $$x+2y$$.

This is under a Cauchy-Schwarz topic, so I'm assuming you have to use the inequality....please help :\]]

Apr 27, 2020

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The minimum value is 2/3.

May 23, 2020