mycroft holmes
Last Activity: 9 Years ago
The missing condition is that x+y+z = 10.
Now, if the numbers were non-negative real numbers, then all we would have to do is use the AP-GP inequality, and in that case the maximum would have happened at x=y=z=10/3. Here x,y,z are natural numbers. So our surest way of maximizing the expression is to therefore choose x,y,z as close to 10/3. Hence we are guided to the triplet (3,3,4) and the expression evaluates to 69