On Thu, 03 Oct 2013 21:05:50 -0400, stony <email@example.com> wrote:
> Hi, I come here once in a while to get some confusions cleared up or > get hints on how to solve something. I teach my daughter who is in > middle school and we come across some problems that stump us. > Any hints would be appreciate. > > The one below, I am missing something in terms of simplifying or some > series or something. Basically, I have tried combining all the terms > after expanding it and could not got to a solution that would simplify > it to prove. It stays in a the expanded form pretty much. > > Prove that: > > ((1/(a^2+1)) + ((1/(b^2+1)) + ((1/(c^2+1)) <= 1/2 > > <= - less than or equal to 1/2 > > I have grouped them together in several ways, but not come close to > simplifying the expanded equation. I thought I could be missing a > simple clue, but cannot come up with it for the past 2 hours. Its not > homework, but practice which she could not do it and I tried it but > have not been able to simplify. Thannks for the help. > > s
-- One reason you might be having a problem is that there is no restriction on the values of a, b, and c. If they are all zero, the inequality is false. Now, assume a, b, and c are all larger than three. Then the inequality is true. (Why?) Inbetween 0 and 3 the inequality becomes dependent upon the relationships between a, b, and c.
Looks to me like a very poor problem to assign to a college student let alone one in middle school.