Anyone can help with this proof please?

[MDTulip]

((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. For example, I want to use the MinValue function. If the minimum value of the left is positive, then it is proven. But how to write the input with the constraint? So if you are familiar with Mathematica, please help!

I really appreciate your time and help.

 

[gb7nash]

That's an insanely long expression. My best advice would be to multiply everything out and see if you get some kind of cancellation. If that doesn't work, you could try mathematica.

 

[MDTulip]

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. :-(

 

[MDTulip]

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 < 1.

Thanks!

That's an insanely long expression. My best advice would be to multiply everything out and see if you get some kind of cancellation. If that doesn't work, you could try mathematica.

 

[MDTulip]

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

 

[blade123]

Don't delete the question! Why would you do that?

People browse these forums all the time soaking up knowledge. Why would you delete it?