three number are in continued praportion whose mean prapotional is 12 and the sum of the remaining two number 26 then find this nu

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three number are in continued praportion whose mean prapotional is 12 and the sum of the remaining two number 26 then find this number.​

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Eloise 2 months 2021-07-27T05:32:50+00:00 1 Answers 0 views 0

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    2021-07-27T05:34:45+00:00

    Step-by-step explanation:

    let the three numbers be a, b and c

    mean proportion in a continued proportion is the number “b”

    when a, b and c are in continued proportion, then

    b² = ac

    given b = 12 and a + c = 26

    therefore 12² = ac

    => 144 = a * (26 – a)

    => 144 = 26a – a²

    => a² – 26a + 144 = 0

    => a² – 18a – 8a + 144 = 0

    => a(a – 18) – 8(a – 18) = 0

    => (a – 18)(a – 8) = 0

    => a = 18 or a = 8

    when a = 18, c = 8

    then three numbers are 18, 12 and 8

    when a = 8, there numbers are 8, 12 and 18

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