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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1. 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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