Ifx= y= z= c/3, then the two sides are equal but that is not true for other values of x, y, z. For example, if x= y= c/4 and z= c/2, then 1/x+ 1/y+ 1/z= 4/c+ 4/c+ 2/c= 10/c and so . The point is that since x= y= z= c/3minimizes1/x+ 1/y+ 1/z, itmaximizesand so maximizes . Since that expression is equal to (1/3)(x+ y+ z)= c/3 when x= y= z= c/3, it cannot be more for any other values of x, y, and z.