Question 1209973
<pre>

I don't believe AI has the right answer.

Let a and b be positive real numbers.  Let

{{{matrix(1,3,

m, ""="",

matrix(1,7,"min[", a, ",", 1/b, ",", b^2+1/(a+1), "]"))}}} 

Find the largest possible value of m.

I can't prove it right off, but my better judgment tells me it's whatever
values of ' a ' and ' b ' that make all three expressions equal, <u>IF</u> there exist
any such values. I'll work on proving it, and if I succeed I'll post it. I hold
an MS degree in mathematics from Clemson University, but I never studied any
such topics as this in any course I ever took.

{{{system(

a=1/b, a=b^2+1/(a+1), 1/b = b^2+1/(a+1) )}}}

WolframAlpha tells me such values do exist, and they are approximately

a=1.1787241761052217926, b=0.848374895731953217

They check with my TI-84 calculator.

So I believe the maximum is approximately 1.1787241761052217926 

Edwin</pre>