The sum of three numbers in AP is 3 and their product is - 35. Find the numbers.

Question

Philoid · Accepted Answer

Let the numbers be (a - d), a, (a + d).

Now, sum of the numbers = 15

∴ (a - d) + a + (a + d) = 3

⇒ 3a = 3

⇒ a = 1

Now, product of the numbers = - 35

⇒ (a - d) × a × (a + d) = - 35

⇒ a³ - ad² = - 35

Put the value of a, we get,

1 - d² = - 35

⇒ d² = 35 + 1 = 36

d² = 36

d = 6

∴ If d = 6, then the numbers are - 5, 1, 7.

If d = - 6, then the numbers are 7, 1, - 5.