The sum of three numbers in AP is 12 and sum of their cubes is 288.Fin

1.	The sum of three numbers in AP is 12 and sum of their cubes is 288.Find the numbers.
Answer» Let the three numbers in A.P. be {tex}a - d, a, a + d{/tex}.{tex}3a = 12 {/tex}or, {tex}a = 4{/tex}.Also, (4 - d)3 + 43 + (4 + d)3\xa0= 288or, 64 - 48d + 12d2- d3 + 64 + 64 + 48d + 12d2 + d3 = 288or, 24d2 + 192 = 288or, 24d2 = 288 - 192or, 24d2 = 96or, d2 = 96/24or, d2 = 4d ={tex}\\pm{/tex}2The numbers are 2,4, 6, or 6,4,2.

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