Q. 254.3( 6 Votes )

# The sum of three

Answer :

To Find: The three numbers which are in AP.

Given: Sum and sum of the squares of three numbers are 21 and 165 respectively.

Let required number be (a - d), (a), (a + d). Then,

(a - d) + a + (a + d) = 21 3a = 21 a = 7

Thus, the numbers are (7 - d), 7 and (7 + d).

But their sum of the squares of three numbers is 165. (7 - d)2 72 (7 + d)2= 165 49 + d2 14d + 49 + d2 + 14d = 116 2d2 = 18 d2 = 9 d = 3

When d=3 numbers are 4, 7, 10

When d= ( 3) numbers are 10, 7, 4

So,Numbers are 4, 7, 10 or 10, 7, 4.

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