Love these kind of problems Just a note though - could you not observe that you need the product of the roots of the quadratic equation, which is given by c/a in 0=ax^2+bx+c, so you know the answer is 26 without having to find the roots then multiply them together?
You could in this case because the quadratic simultaneous equations you get when substituting for X and when substituting for Y are the same. I preferred not to take that shortcut on the off-chance that substituting for Y generated a different quadratic than substituting for X.
I think you could probably solve it geometrically as well, the method I posted was just the one I prefer to use.
At the Nottingham University Open Day there was a "Maths Trail" with several interesting questions on it. The questions ranged from requiring a working knowledge of arithmetic progressions and combinations to lowest common multiples and counting squares; and more emphasis was put on thinking about them than slogging through endless manipulation. I thought I'd share one with you. The question is of the kind that could be set in C1, but is an interesting one:
A rectangle is inscribed inside a circle of radius 6 units such that each of the vertices of the rectangle lie on the circumference of the circle. Given that the perimeter of the rectangle is 28 units, what is the area?
You have the right inverse and are right in the simplification of the original equation. I cannot remember the derivative but your answer looks about right. Any luck with the values of x for which this converges?
I find analysis a bit boring to be honest. I prefer "even purer maths"... They seem to have more depth and involve more creativity.
I have studied a bit of it, and I find it interesting; some of Cauchy's stuff is amazing and I would say it is creative. However, I do get stuck from time to time -- I thought I understood uniform continuity two months ago, but now I have to read it again.
You have the right inverse and are right in the simplification of the original equation. I cannot remember the derivative but your answer looks about right. Any luck with the values of x for which this converges?