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

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Solution

If a,b c are in continued proportions
then b^2 =ac
ac = 144
sum of a and c = a+c = 26
a(26-a) = 144
a^2-26a +144 =0
(a-8) (a-18) = 0
a =8 or a =18
so other numbers are a =8 or a =18
so other numbers are 8 or 18

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