Question

The sum of three numbers in GP is 21/2 and their product is 27. What are the numbers?​
The sum of three numbers in GP is 21/2 and their product is 27. What are the numbers?​

Answer 1

Answer:

let the numbers are a/r,a,ar

here r is the common ratio

so,

a/r.a.ar=27

=> a^3=27=3^3

=> a=3

again,

a/r+a+ar=21/2

=> a(1/r+1+r)=21/2

=> 3(1+r+r^2)/r=21/2

=> 1+r+r^2=7r/2

=> 2+2r+2r^2=7r

=> 2r^2+2r+2-7r=0

=> 2r^2-5r+2=0

=> 2r^2-4r-r+2=0

=> 2r(r-2)-1(r-2)=0

=> (r-2)(2r-1)=0

r-2=0

=> r=2

2r-1=0

=> 2r=1

=> r=1/2

the numbers are 3/2,3,6