Posted by Anonymous on .
the geometric mean of the quantaties (x+1)and (2x+3)is(x+3).
i know that x^2+6x+9=2x^2+5x+3
and
6=x^2x
(i forgot basic algebra)

geometry 
Reiny,
then (x+3)/(x+1) = (2x+3)/(x+3)
crossmultiply
2x^2 + 5x + 3 = x^2 + 6x + 9
x^2  x  6 = 0
(x3)(x+2) = 0
x = 3 or x = 2
if x = 3, the 3 terms are 4, 6, and 9
(note 6/4 = 9/6)
if x = 2, the 3 terms are 0, 1, and 1
but that is not possible, if the first term of a geometric sequence is zero, all the remaining terms would be zero.
so x = 3