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.
antinued proportion.​

Answer 1

let the there numbers be

a,b,c

As they are in continued

Proportion

b² =ac

mean is 12

∴b=12

So, 12² =ac

144=ac

$\sf \: c = \color{purple} \frac{144}{a}$

Sum of two number is

a+c=26

$\sf \: a + \frac{144}{a} = \color {blue}26$

Solving,

=a² +144−26a=0

=a² −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