Question

if the product of 3 numbers in GP is 27 and the sum of their product in pairs is 39 find the numbers.
Pls help​

Answer 1

Answer:-

Let the numbers be a/r , a , ar.

Given:

Product of the numbers = 27

→ (a/r) * (a) * (ar) = 27

→ a³ = (3)³

→ a = 3

And,

Sum of product of the numbers in pairs = 39

→ (a/r) * (a) + (a) * (ar) + (ar) * (a/r) = 39

→ r + a²r + a² = 39

Putting the value of a we get,

→ r + (3)² * r + (3)² = 39

→ r + 9r + 9 = 39

→ 10r + 9 = 39

→ 10r = 39 - 9

→ 10r = 30

→ r = 30/10

→ r = 3

Hence,

• a/r = 3/3 = 1
• a = 3
• ar = 3 * 3 = 9.

Therefore, the three required numbers of the given GP are 1 , 3 , 9.

Verification:-

Product = 27

→ (1) * (3) * (9) = 27

→ 27 = 27

Sum of product of the numbers = 39

→ (1) * (3) + (3) * (9) + (9) * (1) = 39

→ 3 + 27 + 9 = 39

→ 39 = 39

Hence, Verified.