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Let a,b,c,d be non-negative real numbers such that a+b+c+d=1. Find the minimun value of

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Let a,b,c,d be non-negative real numbers such that a+b+c+d=1. Find the minimun value of \(a^2 + b^2 + c^2 + d^2.\)

plz give a solution

Jul 27, 2020

#1
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Can I have help?

Jul 27, 2020
#2
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Sure, I can help you, but maybe be a little more patient next time. Answerers need to take time to solve the problem.

I'm not so sure about my hint, (and I'm not too confindent in my answer) but hopefully it helps you think. For your second expression to be the smallest possible value, the values of the first equation has to have EVERY single value to be the smallest possible. Sure, you could set one value to 1/200000, but then the other values need to be larger. Using number sense, we can see that the most "logical" solution for a, b, c, and d is 1/4, 1/4, 1/4, and 1/4. Notice a pattern? That is right, they are all the same. Adding the squares up will give us (yet again!) 1/4.

ilorty  Jul 27, 2020
#3
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okay, thanks

Guest Jul 27, 2020