Find the smallest possible value of

in terms of the constant k, given that xy=k, and x>y>1.

If xy=k, a constant, finding the minimum of f is the same as finding the minimum of (x^4-2x^2y^2+y^4)/(x^2-y^2)= x^2-y^2, which obviously occurs for minimum x and maximum y, at x=1, y=k.

Thus, the minimum of f is (2k^4-k)/(1-k^2).

Posted by Old Original Oskar! on 2007-03-27 12:48:59