Find the minimum of { (x + 1/x)^{6} - (x^{6} + 1/x^{6}) - 2 }/{ (x + 1/x)^{3} + (x^{3} + 1/x^{3}) }, for x > 0.

**Solution**

*Easy*

Simplifying, we find that the expression is 3(x + 1/x). This has minimum at x = 1, value 6.

© John Scholes

jscholes@kalva.demon.co.uk

12 Dec 1998