## Sunday, January 21, 2007

### 2007. 38

Daily, they'll get harder.  How hard? Try this one:

Difficulty: hard. Especially when you aren't using a calculator.
However, this does mean that the problem is solvable that way and stuff will cancel when you realize the method to use. Of course, when you don't see the method, it's frustrating as hell.

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest

1. So I like the idea. And the first problem. I note a pair of restrictions. And I note one simplification.

Then it looked complicated.

And then I took one guess, just to play and get my hands dirty, and checked, and that was an awfully lucky guess!

Jonathan

2. And looking back, I see a much more efficient simplification, that would have immediately told me the difference between a and b.

Jonathan

3. OK Jonathan, give me a hint. I have the answer, and I got a pretty nice simplification that helped a lot (a relationship between a^2 and b), but I don't see how to find the difference between a and b.