The Area Way Incases , where a relation with areas is possible, It is quite efficient to use it to solve the problem. Example – If are the altitudes of a triangle from A,B,C to the opposite sides and r is the inradius. Prove that – 1. 2. Proof Let I be the incentre. Note […]
With the on-going trend, Algebraic Inequalities are almost erasing the existence of Geometrical Inequalities . Nevertheless, They are equally beautiful (if not more) , although they seem a lot harder to me. Yes, they can mostly be proved by brute-force trigononmetry or complex (whatever it is , they are equally good solutions) , but I […]
Man, i just found out about Loreena Mckennit . She is such a brilliant singer !!!! no more words to describe.. this says it all – http://www.youtube.com/watch?v=S2CFM4ev-g8
Problem Prove that – P.S. It is straightforward holder, but what about a solution by Cauchy or AM-GM ? Solution By, AM-GM we have , Write up analogous inequalities, and add to get – which re-arranges to the desired question 🙂
LockHartsLament The article talks for itself.. Beautifully written.. I wish one day i could put forward my thought in such an organized and calm manner despite the frustrations and anger and emotions..
iSolve : For A,B,C reals Method : Let Choose , rewrite this as – which again is re-written as – Where , Therefore, and are the roots of the equation – Therefore , Now we have that – Solving the quadratic plus the trivial solution gives us – now substituting the value of y in […]
We define is is the exponent of p in the expansion of a. Thus by definition we directly have the following facts – 1. 2. 3. Equality when 4. 5. We also have the legendre’s formula – 6. This function gets to be seriously useful many more plus it is beautiful !! . Setting such […]