To Find: The three numbers which are in AP.
Given: Sum and product of three numbers are 27 and 648 respectively.
Let required number be (a - d), (a), (a + d).
Then,
(a - d) + a + (a + d) = 27
⇒ 3a = 27
⇒ a = 9
Thus, the numbers are (9 - d), 9 and (9 + d).
But their product is 648.
∴ (9 - d) × 9 × (9 + d)= 648
⇒ (9 - d)(9 + d)= 72
⇒ 81 – d2 = 72
⇒ d2 = 9
⇒ d = ± 3
When d = 3 numbers are 6, 9, 12
When d = (– 3) numbers are 12, 9, 6
So, Numbers are 6, 9, 12 or 12, 9, 6.
