SOLUTION: find two positive numbers whose sum is 324 and the sum of those squares is a minimum

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Question 1051039: find two positive numbers whose sum is 324 and the sum of those squares is a minimum
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.A%2BB=324
.
.
2.C=A%5E2%2BB%5E2
From eq. 1,
A=324-B
Substituting into eq. 2,
C=%28324-B%5E2%29%2BB%5E2
C=B%5E2-648B%2B104976%2BB%5E2
C=2B%5E2-648B%2B104976
To minimize C, put it into vertex form,
C=2%28B%5E2-324B%29%2B104976
C=2%28B%5E2-324B%2B26244%29%2B104976-2%2A26244%29
C=2%28B-162%29%5E2%2B52488
So then the minimum sum of the squares of 52488 occurs when B=162 and A=162