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.​

Answer 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