Inspired by Julian Poon and an encyclopedia
Let x , y , z be positive real numbers such that x 2 + y 2 + z 2 = 2 ( x y + y z + z x ) . Find the maximum value of
A = r = 1 ∏ 5 3 ( x r ( r + 1 ) / 2 + y r ( r + 1 ) / 2 + z r ( r + 1 ) / 2 ) x 2 6 2 3 5 + y 2 6 2 3 5 + z 2 6 2 3 5 .
Write your answer in the form of ⌊ 1 0 6 A ⌋ .
The answer is 646147.
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1 solution
Hey, just since I was meditating on the inspiration problem too, did you mean to write x 5 1 2 6 5 6 + y 5 1 2 6 5 6 + z 5 1 2 6 5 6 as the numerator? (where 5 1 2 6 5 6 = 7 1 6 2 = 1 + 3 + 5 + . . . + 1 4 3 1 )
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Ah... No. What I wanted to mention is about the triangular numbers. I'll edit the problem. Thanks.
Sorry for the mistake.
By the way, I've edited the page. Check out.
Thank god @Julian Poon , at least someone got it correct XD
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Ya, @Julian Poon reveal a very good solution, or a very good approximation to solve this kind of problem!
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Now we need a full solution XD
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@Steven Jim – Ya, we need to approach something accurate XD
[Not a solution, as I'm stuck with Julian's problem]
The maximum value is ( 2 + 4 ) ( 2 + 4 3 ) . . . ( 2 + 4 1 4 3 1 ) 2 + 4 2 6 2 3 5 .