question_answer 1)

Find two positive numbers whose sum is 16 and sum of whose cubes is minimum. 

Answer:

Let x and y be the required numbers such that       x + y = 16       and sum of their cubes       S = x3 + y3 = x3 + (16 ? x)3 (Using (1))                               = 6x + 3 × 2 (16 ? x)       = 6(x + 16 ? x) = 96              is minimum when x = 8             Required numbers are 8, 8.