Question

find the three number of GP whose sum is 38and whose product is1728​

Answer 1

Answer:

Let x,y,z be the numbers in geometric progression?

y^2=xz

x+y+z=38

xyz=1728

xyz = xzy = y^2y = y^3 = 1728

y = 12

y^2=xz=144

z=144/x

x+y+z = x+12+144/x = 38

x^2+12x+144=38x

x^2-26x+144=0

(x-18)(x-8)=0

x=8,18

If x =8, z = 38-8-12=18

The numbers are 8,12, 18

Their sum is 38

Their product is 1,728