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.

What is the relationship between the arithmetic, geometric and harmonic means of two numbers, the sides of a right angled triangle and the Golden Ratio?