Question

Find three numbers in GP whose product is 3375 and whose sum is 65.​

Answer 1

Step-by-step explanation:

let the three no. be a/r, a, ar

so, according to the question

a/r+a+ar=65.....equation (1)

a/r×a×ar=3375..... equation (2)

from equation (2) we get,

a^3=3375

a=15

from equation (1) we get

(a+ar+ar^2)/r=65

(a+ar+ar^2)=65r.......equation (3)

sustituing a=15 in equation (3) we get

15+15r+15r^2=65r

15r^2-50r+15=0.......equation(4)

Dividing equation (4) by 5 we get,

3r^2-10r+3=0

3r^2-9r-r+3=0

3r(r-3)-1(r-3)=0

Now the equation will be

15/3,15,15×3

or

15/(1/3),15,15×1/3

so the terms are 5,15,45

The three no are 5,15,45

Thank you

Hope it will help you