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Divide 207 in three parts, such that all parts are in A.P. and product of two smaller parts will be 4623.

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Sol.    Let the 3 parts which are in A. P.
∴       be a – d, a, a + d
         According to condition (I),
        (a – d) + a + (a + d)  =  207
             a – d + a + a + d  = 207
                                    3a = 207

                                      a = \(207\over3\)

                                      a = 69
         According to condition (II)
         (a – d) (a) = 4623
         (69 – d)69 = 4623

               69 – d = \(4623\over 69\)

               69 – d = 67
                       d = 2
           The three parts are,
          (a – d) = 69 –2 = 67,
           a = 69
          (a + d) = 69 + 2 = 71

∴        The three parts are 67, 69, 71

Arithmetic Progression September 28 , 2018 0 Comments 20 views