If a,b,c are in continued proportion.
Prove abc(a+b+c)^3= (ab+bc+ac)^3

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Solution

a,b,c are in continued proportion means
a÷b = b÷c
i.e b^2=ac

Let think about (a+b+c)^3
Simply solve this by taking any two terms in close that means
[(a+b)+c]^3 and apply
(X+y)^3=x^3+y^3+3xy(x+y) equation on that....
then give value for all ac as b^2 as we tell above.
then we get answer as
(a+c+ac÷b)^3

Let think about abc
=ac×b=b^2×b=b^3

final answer is product of b^3 and (a+c+ac÷b)^3.
So final answer is
(ab+bc+ac)^3

do once in a paper...you will get idea..
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