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Let a ,b ,c ,d be four distinct real nu...

Let `a ,b ,c ,d` be four distinct real numbers in A.P. Then half of the smallest positive valueof `k` satisfying `2(a-b)+k(b-c)^2+(c-a)^3=2(a-d)+(b-d)^2+(c-d)^3` is __________.

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