Q. 3 A5.0( 2 Votes )

Divide 15 into three parts which are in A.P. and the sum of their squares is 83.

Answer :

Let the middle term = a and the common difference = d


The first term = a – d and the succeeding term = a + d


So, the three parts are a – d, a, a + d


According to the question,


Sum of these three parts = 15


a – d + a + a + d = 15


3a = 15


a = 5


and the sum of their squares = 83


(a – d)2 + a2 + (a + d)2 = 83


(5 – d)2 + (5)2 + ( 5 + d)2 = 83 [from(i)]


25 + d2 – 10d + 25 + 25 + d2 + 10d = 83


75 + 2d2 = 83


2d2 = 83 – 75


2d2 = 8


d2 = 4


d = √4


d = ±2


Case: (i) If d = 2, then


a – d = 5 – 2 = 3


a = 5


a + d = 5 + 2 = 7


Hence, the three parts are


3, 5, 7


Case: (ii) If d = – 2, then


a – d = 5 – ( – 2) = 7


a = 5


a + d = 5 + ( – 2) = 3


Hence, the three parts are


7, 5, 3


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