If only the world community knew this fact, they would not be devoting so much time to proving all sorts of inequalities, finding maxima, minima etc.

 

That kind of approach is quite ok in many situations for guessing the answer when it is objective type, but when a proof is sought that sort of generalisation simply wont do.

 

e.g. a+b+c+d = 1, what is the minimum value of 1/a+1/b+4/c+16/d (all +ve)

 

By the way since this topic has been revived, this inequality can be done by a combination of Chebyshev's inequality and Nesbitt's Inequality( a/b+c3/2) Anybody game?

 

Hint:  Chebyshev's inequality is a very close cousin of RI