Thread: (x^2 + y^2)/xy > 2
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Old November 3rd, 2009, 06:45 PM
alexmahone alexmahone is offline
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Quote:
Originally Posted by Jazz10 View Post
(x^2 + y^2)/xy = x/y + y/x > 2. I can clearly see why this is true, but can't find a proof, need this as a lemma to a harder problem. Any help is appreciated.
\frac{\frac{x}{y}+\frac{y}{x}}2\geq\sqrt{\frac{x}{y}\frac{y}{x}} (By AM-GM inequality)

\frac{x}{y}+\frac{y}{x}\geq2
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