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

Answer is here.

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

ReplyDeleteThen 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

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

ReplyDeleteJonathan

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.

ReplyDeleteStart with equation 2 and solve for b².

ReplyDeleteIf you start with the second equation, you can express both sides as perfect squares.

ReplyDeleteAhh! Nice--thanks.

ReplyDelete