quadratic function
2009-11-29 5:03 am
given that the sum of 2 positive number is 10, find the numbers so that the sum of their squares is a minimum.
回答 (1)
2009-11-29 5:40 am
✔ 最佳答案
Let one of the number = xthe other number will be = 10 - x
So sum of their square, y = x^2 + (10 -x)^2 = x^2 + 100 + x^2 - 20x
= 2x^2 - 20x + 100
= 2(x^2 - 10x + 50)
= 2[(x - 5)^2 + 25]
= 2(x - 5)^2 + 50
so the number is 5, minimum is 50.
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