Split 207 into three parts such that these are in AP and the product of the two smaller parts is 4623.

Let the three parts of the number 207 are


a1 = a - d


a2 = a


a3 = a + d


Clearly a1, a2 and a3 are in AP with common difference as d.


Now, by given condition,


Sum = 207


a1 + a2 + a3 = 207


(a - d) + a + (a + d) = 207


3a = 207


a = 69


Also,


a1a2 = 4623


(a - d)a = 4623


(69 - d)69 = 4623


69 - d = 67


d = 69 - 67


d = 2


Hence, required three parts are 67, 69, 71.


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