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Let a_1, a_2, ..., a_{20} be real numbers such that

a_1 + 2a_2 + ... + 20a_{20} = 1,

and a_1^2 + 2a_^2 + ... + 20a_{20}^2 is minimized.  Find a_{12}.

 Aug 16, 2021
 #1
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a_{12} = 10*sqrt(3)/3.

 Aug 16, 2021

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