Question 1209896
<pre>

Let x and y be real numbers. Find the maximum value of (x + y)^2,
if x and y satisfy x^2 + y^2 = 5 + 2xy.

Add 2xy to both sides of 

{{{x^2 + y^2 = 5 + 2xy}}}

{{{x^2+2xy+y^2 = 5 + 4xy}}}

{{{(x+y)^2 = 5 + 4xy}}}

The left side is what we want to find a maximum value for.  But! --- see the
+4xy term on the right? You can choose x and y each to be a trillion trillion
trillion trillion and even that would not be anywhere close to being a maximum
value for {{{(x + y)^2}}}.

Answer:  There is no maximum value for {{{(x + y)^2}}}!

Edwin</pre>