2)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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Step-by-step explanation:
Let , three numbers a,b,and c are in continued proportion .
∴ a:b:c that is
b² = ac
∵ mean is 12
∴12²=ac
144= ac
∴c = 144/a
now sum of remaining two numbers is 26
∴ a+c = 26
a+144/a =26
a²+144 = 26a
a²- 26a +144 =0
a²-18a -8a+144 =0
a(a-18) - 8(a-18) =0
(a-18) (a-8) =0
∴ a=18 or a= 8
∴either a=18 and c=8 or a=8 and c= 18
∴ those numbers are 8,12,18 or 18,12,8
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