Question

Three numbers and in continued proportion, whose mean
proportional is 12 and the sum of the remaing
two numbers
is 26, the
find these numbers​

Answer 1

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 numbers 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