Well I have found a factorisation of this algebraic expression on a website. It just reduces the expression to something which easily leads us to believe that the inequality is true. Here's the link :
http://smc.math.ca/crux/v31/n8/public_page492-499.pdf
Homework Statement
Let a,b,c be positive real numbers. Prove that:
a3+b3+c3≥a2b+b2c+c2a
Homework Equations
The Attempt at a Solution
I assumed that a≥b≥c>0 following which I shifted the left side of this inequality to the right side giving
a3+b3+c3-(a2b+b2c+c2a)≥0
How...
When I calculated for the case when all balls go to only 2 people --->
The possible set is (2,3,0)
So, Applying combinations 5C2 * 3C3 = 10
also, the elements of the set can be arranged among themselves in 6 ways therefore my answer turns out 6*10 = 60 . How did you get 90 ...
Ya, you are right ... thanks for helping me figure out the error. I believe first part of the solution is all right ... and the second part has an error as you pointed. But how can it be corrected? Also I have found a similar question like that and again the same problem. First you please let me...
I have understood the whole thing you all want to say and I am going to attempt it once more. But I am still not getting why my approach doesn't hit the point...
As mfb replied that it's 60*9, I agree with that but how does it count outcomes twice? please explain it ...
Homework Statement
The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball is ...
Homework Equations
The Attempt at a Solution
I began by finding the number of ways of distributing 5 balls among...
I understand why we use sign convention ... but what's the need of using the sign convention once again ? We have already used the sign convention while deriving the formula for a lens.
I googled for lens formula's proof on the internet and found one here
http://www.tutorvista.com/content/physics/physics-ii/light-refraction/convex-lens-formula.php
The problem is that during the course of derivation, it is assumed that image distance is -u following the sign convention...
I read in a book that an aqueous solution of ethanol produces a constant-boiling mixture which contains 95.6% ethanol and 4.4% water. This is called rectified spirit.
I googled the word "constant-boiling" and I came to the conclusion that it's nothing but azeotrope. But it isn't clear to me...
I read somewhere that the focus of a plane mirror is at infinity because rays after reflection from a plane mirror don't intersect anywhere. But why can't the focus be virtual as in case of concave mirror ?
Basically, I want to know how do I find the valency of copper by writing the electronic configuration like I wrote for Sodium. [Ne]3s1. Here, I find that sodium's valency is 1 which is in 3s1. But how do I do the same for copper ?
Writing the electronic configuration of Cu :
[Ar] 4s13d10, I feel that the number of valence electrons in a copper atom is 11. But it doesn't make any sense to me why copper has a valence of 1 or 2 as in case of CuSO4 ... which is 2.
Going the usual way, if we consider Sodium, which has an...