Q. 284.8( 19 Votes )

The sum of three

Answer :

It is given in the question that, sum of three A.P. = 12

Also, Sum of cubes of three A.P. = 288


Let us assume the three numbers in A.P. are a – d, a and a + d


a – d + a + a + d = 12


3a = 12



Also, (a – d)3 + (a)3 + (a + d)3 = 288


a3 – 3a2d + 3ad2 – d3 + a3 + a3 + 3a2d + 3ad2 + d3 = 288


3a (a2 + 2d2) = 288


3 × 4 (4 × 4 + 2 × d × d) = 288



2d2 = 8


d2 = 4



Now, when the value of a = 4 and d = 2 then the numbers will be:


a – d = 4 – 2 = 2


a = 4


a + d = 4 + 2 = 6


Or, when a = 4 and d = - 2 then the numbers will be:


a – d = 4 – (- 2) = 6


a = 4


a + d = 4 + (- 2) = 2

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