Question

Find three numbers in G.P.,whose sum is 19 and product is 216

Answer 1

Let three numbers be x/r , x and xr....
Product = x^3 = 216
x = (216)^1/3
x = 6
x/r + x + xr = 19
Putting value of x...
6/r + 6 + 6r = 19
6 + 6r + 6r^2 = 19r
6r^2 - 13r + 6 = 0
6r^2 -9r -4r + 6 = 0
3r(2r-3) -2(2r-3) = 0
(3r-2)(2r-3)=0
3r-2=0. 2r-3=0
r= 2/3. r= 3/2
Then numbers are...
9, 6 and 4
and
4, 6 and 9
Above are required numbers ...
THANKS