Notice first that: \frac{a^3}{(2a^2+b^2)(2a^2+c^2)}=\frac{1}{a}\frac{1}{(2+\frac{b^2}{a^2})(2+\frac{c^2}{a^2})} Since,(2+\frac{b^2}{a^2})(2+\frac{c^2}{a^2})=(1+1+\frac{b^2}{a^2})(1+\frac{c^2}{a^2}+1)\ge(1+\frac{c}{a}+\frac{b}{a})^2=\frac{(a+b+c)^2}{a^2} ...

With the help in the comments, I have solved the problem correctly, and checked it with Mathematica. I'll post my solution here, it might be useful to someone who might stumble upon this post. My ...

Step 6 is indeed redundant. One can see that the argument used in Step 6 is essentially identical to that used for proving the 1-1 property of A. Evans might just think it is clearer for students ...

This is called the glove game. When a=b you need to make sure that all of the people with right shoes get the same amount of cash and you need to make sure that all the people in the left get the ...

(S) has a unique solution f(x)=\int_0^x (x-t)\,g(t)\,dt+a+ct, where c=b-\int_0^1 (1-t)\,g(t)\,dt-a.

First, \cap_{N=1}^{\infty} ( \cup_{n=N}^{\infty} A_n) = \infty makes no sense as a set can be of infinite cardinality but not be equal to infinity. Now regarding your task: I assume that there is ...