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Equal and Greater (Posted on 2024-08-23)

Suppose that for all reals 0 ≤ a ≤ b ≤ c ≤ d , we have :

(a + b + c + d)^2 ≥ K*b*c

Find the largest possible value of K.

No Solution Yet Submitted by K Sengupta

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possible answer

| Comment 1 of 2

I suspect the answer is 9.

Suppose a = 10^-n

and b = c = d = 10^n

where n is a large positive number.

LHS: (3*10^n + ε)^2 = 9*10^2n + 6ε*10^n

RHS: K*10^2n

essentially: 9*10^2n >= K*10^2n

9 >= K

Posted by Larry on 2024-08-23 17:25:20

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