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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
(i forgot basic algebra)

  • geometry -

    then (x+3)/(x+1) = (2x+3)/(x+3)
    2x^2 + 5x + 3 = x^2 + 6x + 9
    x^2 - x - 6 = 0
    (x-3)(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

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