LEt x=1, y=2,a=1, b=-1
So is false,
so what are the restrictions on x,y,a,b, are they all positive, are just a,b>0... we need more info otherwise I just gave you a counterexample meaning its false
I don't know, it has variables in it... Ugh finding a section is hard.
Prove
because I moved countries a lot when I was little I think I missed out on most of the fraction axioms taught in elementary (took me to the end of high school to figure out cross multiplication >.>) so it might be that I'm missing some fundamental rule here...
i dont think it's proof by induction, although we could just let c=ab for some c>0 but that is still 3 variables
Let's go with this
Consider
If then , so and so the inequality holds
If , then so and so
And so (note that everything we divided by was >0 so that argument really is valid)
If ab(y-x)<0 then x>y since ab>0. So and just looking ahead this fails your inequality meaning we must place the restriction that x cannot be >y
For example let x=4 a=1 b=1 and y=1
Then
and 2.5 is not