Question

find 3 numbers in GP whose sum is 19 and products is 216

Answer 1

Let three numbers be a/r ,a and ar . a/r+a+ar=19......(1) a/r×a×ar=216 a^3=216 a=6.......(2) from 1). 6/r+6+6r=19 6r^2-13r+6=0 6r^2-9r-4r+6=0 3r(2r-3)-2(2r-3)=0 (3r-2)(2r-3)=0 so r=2/3,3/2.  case1) when r=2/3,a=6 then numbers :9,6,4 case2) : when r=3/2,a=6 then numbers :4,6,9  Plz mrk as brainlest if helped