<s>[INST] Sum of the squares of numbers 
Let $x$ and $y$ be the two numbers so that:
$$x^2 + y^2 = A^2$$
$$xy = A^2 + 2A + 2$$
$$xy - x^2 - y^2 = 2A + 2$$
$$\frac{xy - x^2 - y^2}{2} -1 = A$$
So what can I do?
 [/INST] You have:
$$x^2+y^2=A^2$$
$$2xy=2A^2+4A+4$$
So:
$$x^2-2xy+y^2=-A^2-4A-4$$
$$(x-y)^2=-(A+2)^2$$
We know that $(x-y)^2 \geq 0$ and $-(A+2)^2 \leq 0$, so there is one possible value of $A$, it's $A=-2$. 
Substitute A = -2 back into the both equations to get $$x^2+y^2=4$$ $$2xy = 4$$
Subtract the two equations to get $(x-y)^2=0$ => $x=y$.
Put this back in the first equation to get $x = y = \pm\sqrt{2}$.
</s>