Recent content by MDTulip

Ok, I have found the solution. Do not know how to delete here. Please help me delete the question. Thanks.

Okay, let me simlify the expression of my question this way: Let A =(1+R)〖(-4+R^2)〗^2 B =〖(6+4R+B^2 R-5R^2-R^3+R^4+B(R^2+R-2))〗^2 C =(1+γ)〖(-4+γ^2)〗^2) D =〖(6+4γ+β^2 γ-5γ^2-γ^3+γ^4+β(γ^2+γ-2))〗^2 ) I want to prove that A /4B - C /9D > 0, given 0 < γ < R < 1, 0 < β < B <...

Yes it is insanely long. The first part and the second part actually share the same function except that the veriables in the first part are R and B, while in the second part are Beta and r. I cannot just multiply everything because there is a division in both parts. :-(

((1+R)〖(-4+R^2)〗^2)/(4〖(6+4R+B^2 R-5R^2-R^3+R^4+B(-2+R+R^2))〗^2 )-((1+γ)〖(-4+γ^2)〗^2)/(9〖(6+4γ+β^2 γ-5γ^2-γ^3+γ^4+β(-2+γ+γ^2))〗^2 )>0, where 0 < γ < R < 1, 0 < β < B < 1. If you can give me some hints about proving it directly, that will be great. Or, Proving it with Mathematica is also ok...