In Geometric progression the sum of first of three terms is 28 and the product is 512 find those numbers

Answer 1

a+ar+ar^2=28
a^3 * r^3=512

one the second equation, take the cube root of each side.
ar=cubrt(512)=8

a+8+ar^2=28
a(1+r^2)=20

but a= 8/r
8(1+r^2)=20r
8r^2-20 r+8=0

r=(20)+-sqrt(400-256) /16

r=20+- sqrt(144) /16 = (20+-12)/16=2 or 1/2

then a= 4 or 16

check a=4, r=2

4 + 8 + 16=28
a^3 r^3=64*8=512 checks, a=4, r=2

check a=8, r=1/2
8 +4 + 2 does not check.