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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 numbers.

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Solution

Let ad,a,a+d are the three numbers

Here 3a=12

a=4.

Also (ad)3+a3+(a+d)3=288,

3a3+6ad2=288

24d2=2883×64=96

d2=4 or d=±2

Hence the numbers are 2,4,6 or 6,4,2.

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