Question

Find three numbers in G.P. such that their sum is 28 and their product is 512.

Answer 1

Answer:

Step-by-step explanation:

Let the three numbers in GP be a/r,a,ar

sum=a/r+a+ar=28

product=a/r*a*ar=a^3=512

a^3=512

a^3=8^3

a=8

8/r+8+8r=28

8/r+8r=28-8=20

1/r+r=20/8

1/r+r=5/2

(1+r^2)/r=5/2

2+2r^2-5r=0

solving the quadratic equation

2r^2-5r+2=0

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

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

r=2,1/2

now the terms are 8/2,8,8*2=4,8,16