Question

if the sum of three numbers are in AP is 9 and their product is 24 then number are​

Answer 1

EXPLANATION.

Sum of three numbers are in A.P.

Sum = 9.

Products = 24.

As we know that,

Three numbers are in A.P.

⇒ a - d, a, a + d.

Sum of three numbers = 9.

⇒ a - d + a + a + d = 9.

⇒ a + a + a = 9.

⇒ 3a = 9.

⇒ a = 3.

Products of three numbers = 24.

⇒ (a - d)(a)(a + d) = 24.

⇒ (a - d)(a + d)(a) = 24.

⇒ (a² - d²)(a) = 24.

⇒ [(3)² - d²](3) = 24.

⇒ (9 - d²)(3) = 24.

⇒ 27 - 3d² = 24.

⇒ - 3d² = 24 - 27.

⇒ - 3d² = - 3.

⇒ d² = 1.

⇒ d = √1.

⇒ d = ± 1.

When a = 3 and d = 1.

⇒ a - d, a, a + d.

⇒ 3 - 1, 3, 3 + 1.

⇒ 2, 3, 4.

When a = 3 and d = - 1.

⇒ a - d, a, a + d.

⇒ 3 - (-1), 3, 3 - 1.

⇒ 3 + 1, 3, 3 - 1.

⇒ 4, 3, 2.

                                                                                                                       

MORE INFORMATION.

Supposition of an A.P.

(1) = Three terms as : a - d, a, a + d.

(2) = Four terms as : a - 3d, a - d, a + d, a + 3d.

(3) = Five terms as : a - 2d, a - d, a, a + d, a + 2d.