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Given a curve \(128x^2 - 16x^2y + 1 = 0\), how do you find the minimum value of \((x+y)\)?

Is it possible to do this?

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Compute \[\frac{-1}{2^{2011}}\sum_{k=0}^{1006}(-1)^k3^k\binom{2012}{2k}\].

This question came from the Singapore Maths Olympiad 2012 Open Section Round 1.

In the diagram, the two circles intersect at P and Q. AB and CD are common tangents to the circles and PQ produced meets AB and CD at M and ...

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