Given that u>0 and v>0 find the smallest possible value of
1/u + 1/v given that u + v = 5 by different methods.
If x + y = -1 find the largest value of xy by coordinate geometry, by calculus and by algebra.
Use the diagram to investigate the classical Pythagorean means.
Published July 2001,September 2001,February 2011.
The details of this proof are given in the
solution to the problem Pythagorean Golden Means.