Given the equation and , determine the range of value of such that the two graphs intersect at exactly two distinct points.

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- Feb 26th 2011, 04:05 AMPunchtwo distinct points
Given the equation and , determine the range of value of such that the two graphs intersect at exactly two distinct points.

- Feb 26th 2011, 06:08 AMSoroban
Hello, Punch!

Quote:

. .

. .

- Feb 26th 2011, 01:58 PMWilmer
- Feb 26th 2011, 06:59 PMPunch

I tried another method which was to sub equation [1] into [2] and equating the discriminant, but it didn't work. Here's my working.

http://i952.photobucket.com/albums/a...g/P2240112.jpg - Feb 26th 2011, 07:18 PMWilmer
Your 272a^4 + 17152a^2 simplifies to 16a^2(17a^2 + 1072),

which is same as what I showed you in my previous post. - Feb 26th 2011, 07:41 PMPunch
- Feb 26th 2011, 07:47 PMPunch
Also, is it possible to show how you could transform into ?

- Feb 26th 2011, 09:22 PMWilmer
- Feb 26th 2011, 09:46 PMPunch