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

Question

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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Mathematics
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2021-07-27T05:32:50+00:00
2021-07-27T05:32:50+00:00 1 Answers
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## Answers ( )

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