For two distinct positive numbers (a) \(x+y> 2\sqrt{xy}\)(b) \(\cf

1.	For two distinct positive numbers (a) \(x+y> 2\sqrt{xy}\)(b) \(\cfrac{x+y}{2}>xy\)(c) \(\sqrt{xy}> \cfrac{x+y}{2}\)(d) \(\cfrac{2xy}{x+y}> \sqrt{xy}\)
Answer» Correct answer is: (a) \(x+y> 2\sqrt{xy}\) For distinct x, y > 0; AM > GM ⟹ \(\cfrac{x+y}{2}\) > \(\sqrt{xy}\) ⇒ x +y > 2\(\sqrt{xy}\)

For two distinct positive numbers (a) \(x+y> 2\sqrt{xy}\)(b) \(\cfrac{x+y}{2}>xy\)(c) \(\sqrt{xy}> \cfrac{x+y}{2}\)(d) \(\cfrac{2xy}{x+y}> \sqrt{xy}\)

Answer»

Correct answer is: (a) \(x+y> 2\sqrt{xy}\)

For distinct x, y > 0;

AM > GM

⟹ \(\cfrac{x+y}{2}\) > \(\sqrt{xy}\)

⇒ x +y > 2\(\sqrt{xy}\)

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For two distinct positive numbers (a) \(x+y&gt; 2\sqrt{xy}\)(b) \(\cfrac{x+y}{2}&gt;xy\)(c) \(\sqrt{xy}&gt; \cfrac{x+y}{2}\)(d) \(\cfrac{2xy}{x+y}&gt; \sqrt{xy}\)

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For two distinct positive numbers (a) \(x+y> 2\sqrt{xy}\)(b) \(\cfrac{x+y}{2}>xy\)(c) \(\sqrt{xy}> \cfrac{x+y}{2}\)(d) \(\cfrac{2xy}{x+y}> \sqrt{xy}\)