math
posted by Dhanalakshmi .
In Geometric progression the sum of first of three terms is 28 and the product is 512 find those numbers

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^220 r+8=0
r=(20)+sqrt(400256) /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.
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