Question

If positive no. a, b and C is in G.P. then prove that a+b>2b ​

Answer 1

The question posed here is wrong. Its not always possible for 4 numbers in GP to satisfy the above inequality. If a,b,c,d are in GP then they can be represented as a, a*r, a*r^2, a*r^3(r is the common ratio). Plugging this in the above inequality gives us a cubic equation in r telling us that it will always be positive/negative(depending on whether a is positive/negative) for any r(the common ratio). Now, that is not possible!

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