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Question

The sum of three numbers in A.P. is 12 and the sum of their cubes is 288. Find the sum of their squares.

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Solution

Let a,ad and a+d is the A.P
Given 3a=12a=4
Also (ad)3+a3+(a+d)3=288,
or
3a3+6ad2=288 or 24d2=2883×64=96 d2=4 or d=±2
Hence the numbers are 2,4,6 or 6,4,2.

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