Three numbers are in A.P. If the sum of these numbers be 27 and the product648, find the numbers.

Given:

Sum = 27

Product = 648

Let the three numbers be a – d, a, a+ d.
Therefore,

a – d + a + a + d = 27
⇒ 3a = 27
⇒ a = 9
And,

(a – d)(a)(a + d) = 648
⇒ a(a ² – d ² ) = 648
⇒ 9(9 ² – d ² ) = 648                                   [ ∵ a = 9]
⇒ 9 ² – d ² = 72
⇒ d ² = 81 - 72
⇒ d ² = 9
⇒ d = 3
Hence, The numbers are 6, 9, 12.