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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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