Answer to Question #34111 in Functional Analysis for Nathaniel Ruiz

Question

Find the product (x+y+z)(1/x+1/y+1/z) and deduce that the least value of this product, over non-negative x,y, and z, is 9. Use this to find the least value of the function f(x,y,z) = 1/x+1/y+1/z, over non-negative x,y, and z, having a constant sum C.