Posted by **David** on Wednesday, April 10, 2013 at 9:58pm.

Two non-negative numbers are chosen such that their sum is 30. Find the numbers if the sum of their squares is to be a maximum.

Explanation to solve this would help !

- math -
**Steve**, Thursday, April 11, 2013 at 5:25am
m+n=30

m^2+n^2 = m^2+(30-m)^2 = 2m^2 - 60m + 900

Now, that's a parabola with vertex at (15,450)

Since the parabola opens upward, 450 is the minimum, and any maximum will be at the ends of the interval. We can't have m=0, so pick the numbers 1 and 29.

1^2+29^2 = 842

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