Q. 3 A5.0( 2 Votes )

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

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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