Find two positive numbers whose sum is 100 and the sum of whose squares is a minimum.

Question

Mathematics

Nehemiah Bailey

4 July, 13:28

Find two positive numbers whose sum is 100 and the sum of whose squares is a minimum.

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Answers (1)

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Galloway · Answer 1

Let the two required numbers be x and 100 - x, then

Sum of its squares is given by S = x^2 + (100 - x) ^2

For the sum of the squares to be minimum, dS/dx = 0

dS/dx = 2x - 2 (100 - x) = 0

2x - 200 + 2x = 0

4x = 200

x = 50.

The two numbers is 50 and 50.