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