Question

three numbers are in continuined proportion, whose means proportional is 12 and the sum of remaining two numbers is 26, then find these numbers​

Answer 1

Answer:

Let the first number be x. ∴ Third number = 26 – x 12 is the mean proportional of x and (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.Read more on Sarthaks.com - https://www.sarthaks.com/847614/three-numbers-continued-proportion-whose-mean-proportional-and-the-sum-remaining-numbers

hope it helps u

Answer 2

Answer:

The numbers are :-  

8,12,18 or 18,12,8

Step-by-step explanation:

let the there numbers be  a,b,c  

As they are in continued  Proportion  

b^2 =ac

mean is 12

∴b=12

So, 12^2 =ac

144=ac

c=144/a

Sum of two number is

a+c=26

a+144/a =26

Solving,  

=a^2 +144−26a=0

=a^2 −18a−8a+144=0

=a(a−18)−8(a−18)=0

=(a−18)(a−8)=0

∴a=18 or a=8

c=8  c=18

∴ The numbers are :-  

8,12,18 or 18,12,8