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Topic: math problems - help
Replies: 5   Last Post: Oct 4, 2013 7:14 PM

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William Elliot

Posts: 1,481
Registered: 1/8/12
Re: math problems - help
Posted: Oct 4, 2013 1:22 AM
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On Fri, 4 Oct 2013, wilson wrote:
> On Thu, 03 Oct 2013 21:05:50 -0400, stony <x@x.com> wrote:

> > Prove that:
> >
> > ((1/(a^2+1)) + ((1/(b^2+1)) + ((1/(c^2+1)) <= 1/2
> >
> > <= - less than or equal to 1/2


> 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.


If the prosition is true, then 1/a^2 + 1 < the expression <= 1/2
and 1/(a^2 + 1) < 1/2 iff 2 < a^2 + 1 iff 1 < a^2 iff 1 < |a|.

If a = b = c, then expression = 3/(a^2 + 1) and
3/(a^2 + 1) <= 1/2 iff 6 <= a^2 + 1 iff 5 <= a^2 iff sqr 5 <= |a|.

The propsition is false, if any one of a,b or c is between -1 and 1
and true if all three are at least sqr 5 or at most -sqr 5.




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