Quadratic-quadratic minimum

Calculus Level 3

\[\large \left(1+\left(r+\frac{1}{r}\right)^2\right)x^2- 6\left(r+\frac{1}{r}\right) x+\left(r+\frac{1}{r}\right)^2+4\]

Find the absolute minimum value of the given expression, where \(x\) and \(r\) take any real value and \(r\not =0.\) If you think that it does not have an absolute minimum value, enter 0.

If you get to solve this problem, you might want to try one of the IMO73 problems.That problem has been posted here.

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