Three numbers are in AP. If their sum is 27 and their product is 648,

1.	Three numbers are in AP. If their sum is 27 and their product is 648, find the numbers.
Answer» 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.

Three numbers are in AP. If their sum is 27 and their product is 648, find the numbers.

Answer»

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.