Question is: Find two nonnegative numbers whose sum is 1 such that the sum of their squares is a minimum.

I have the following:

x^2 - y^2 = s
s = x^2 + (1 - x)^2
ds = 2x + 2(1 - x)(-1) = 0
= 2x + 2 (-1 + x) = 0
= 2x - 2 + 2x = 0
= 4x - 2 = 0
x = 1/2

Am I wrong?

Question

Question is: Find two nonnegative numbers whose sum is 1 such that the sum of their squares is a minimum.

I have the following:

x^2 - y^2 = s
s = x^2 + (1 - x)^2
ds = 2x + 2(1 - x)(-1) = 0
     = 2x + 2 (-1 + x) = 0
     = 2x - 2 + 2x = 0
     = 4x - 2 = 0
 x = 1/2

Am I wrong?

anonymous · Answer

looks correct to me :)  you have minus sign in your first line, must be a typo though (since you switched it to a plus in the second line).
Answer is correct though.

anonymous · Answer

Yeah, that was a typo. I did it a little different from what I was shown, so I just wanted to be sure. Thanks!!  :)