Question

Three numbers are in ap if the sum of these numbers be 27 and the product 648

Answer 1

Three numbers in A.P. if the sum of these numbers be 27 and the product 648 are  6, 9 & 12 or 12, 9 & 6.

Step-by-step explanation:

Let the three terms in A.P. be (a-d), a & (a+d).

Step 1:

The sum of three terms = 27 …. [given]

Therefore,

⇒ (a-d) + a + (a+d) = 27

⇒ 3a = 27

⇒ a = $\frac{27}{3}$

⇒ a = 9 …….. (i)

Step 2:

The product of three terms = 648 …….. [given]

Therefore,

[a-d] * a * [a+d] = 648

⇒ [a² - d²] * a = 648

⇒ [9² - d²] * 9 = 648 ……. [ substituting value of a from (i)]

⇒ 81 - d² = $\frac{648}{9}$

⇒ 81 - d² = 72

⇒ d² = 81 – 72

⇒ d² = 9

⇒ d = ±3

Step 3:

(1). When a = 9 & d = 3 :

Then the 3 numbers are:

a - d = 9 - 3 = 6

a = 9

a + d = 9 + 3 = 12

(2). When a = 9 & d = -3 :

Then the 3 numbers are:  

a-d = 9 -(-3) = 9+3 = 12

a = 9

a+d = 9+(-3) = 9-3 = 6

Thus, the 3 numbers in A.P. are 6, 9 & 12 or 12, 9 & 6.

---------------------------------------------------------------------------------------------

Also View:

The sum of numbers lying between 10 and 200 which are divisible by 7 will be?

https://brainly.in/question/5422286

Arithmetic progression question  

https://brainly.in/question/8483912

The tenth term of the arithmetic progression whose sum n² – 3n.

https://brainly.in/question/9162282

Answer 2

Answer:

the numbers are 6,9,12 or 12,9,6

I hope it will surely help you..

$...$