Question 424577
We have two numbers, {{{a}}} and {{{40-a}}} and want to minimize the sum {{{a^2 + (40-a)^2}}}, or {{{2a^2 - 80a + 1600}}}. The parabola's leading coefficient is positive, so the minimum value occurs at the "vertex," which occurs when {{{a = 80/(2(2)) = 20}}}. Thus, {20,20} minimizes the sum and this sum is {{{20^2 + 20^2 = 800}}}.