Question

three numbers whose sum is 15 in AP. if 1,3,9 are added respectively to the numbers the resulting number are in GP. find the numbers​

Answer 1

Answer:

solved

Step-by-step explanation:

let the numbers be: a-d , a , a+d

3a = 15 , a = 5

the number are : 5-d , 5 , 5+d

then by adding 1, 3 , 9

the new numbers will be : 6-d , 8 , 14+d ,  

64 = ( 14+d ) (6-d   ) = 84 - 8d - d²

d²+ 8d - 20 = 0

(d +10)(d-2) = 0

d = -10 , 2

case 1 , d = -10

the numbers are 15 , 5 , -5

case2 , d = 2

the numbers are 3 , 5 , 7