Question

Three numbers are in continued proportion, whose mean proportional is 12 and the sum of the remaining two numbers is 26, then find these numbers.

Answer 1

Let the first number be x. 

∴ Third number = 26 – x 

12 is the mean proportional of x and (26 – x).

∴ \(\frac{x}{12}\) = \(\frac{12}{26-x}\)

∴ x(26 – x) = 12 x 12 

∴ 26x – x² = 144 

∴ x² – 26x + 144 = 0 

∴ x² – 18x – 8x + 144 = 0 

∴ x(x – 18) – 8(x – 18) = 0

∴ (x – 18) (x – 8) = 0 

∴ x = 18 or x = 8 

∴ Third number = 26 – x = 26 – 18 = 8 or 26 – x 

= 26 – 8 = 18 

∴ The numbers are 18, 12, 8 or 8, 12, 18.