Question

The sum of three numbers in a GP is 26.
and their product is 216. Find the numbers.​

Answer 1

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Answer....

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Solution :

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

=> (a / r) + a + a r = 26

=> a (1 + r + r2) / r = 26

Also, it is given that product = 216

=> (a / r) x (a) x (a r) = 216

=> a3 = 216

=> a = 6

=> 6 (1 + r + r2) / r = 26

=> (1 + r + r2) / r = 26 / 6 = 13 / 3

=> 3 + 3 r + 3 r2 = 13 r

=> 3 r2 – 10 r + 3 = 0

=> (r – 3) (r – (1 / 3) ) = 0

=> r = 3 or r = 1 / 3

Thus,

the required numbers are 2, 6 and 18.

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Answer 2

Answer:

refer to the above attachment for the solution...