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- Jan 26, 2012

- 4,055

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Remember to read the POTW submission guidelines to find out how to submit your answers!

- Thread starter Jameson
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- Thread starter
- Admin
- #1

- Jan 26, 2012

- 4,055

--------------------

Remember to read the POTW submission guidelines to find out how to submit your answers!

- Thread starter
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- #2

- Jan 26, 2012

- 4,055

1) MarkFL

2) anemone

3) Pranav

4) eddybob123

5) kaliprasad

Solution (from eddybob123):

$$\Rightarrow 71>2\sqrt{1260}$$

$$\Rightarrow 1< 72-2\sqrt{1260}$$

$$\Rightarrow 1^2< (\sqrt{42}-\sqrt{30})^2$$

$$\Rightarrow 1< \sqrt{42}-\sqrt{30}$$

$$\Rightarrow 2<2(\sqrt{42}-\sqrt{30})$$

$$\Rightarrow 7-2\sqrt{42}+6<6-2\sqrt{30}+5$$

$$\Rightarrow (\sqrt{7}-\sqrt{6})^2<(\sqrt{6}-\sqrt{5})^2$$

$$\Rightarrow \sqrt{7}-\sqrt{6}<\sqrt{6}-\sqrt{5}$$

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