<s>[INST] find pairs of real numbers $x, y$ to satisfy this equation equation is:    $(x + y)^2 = (x + 3)(y − 3)$
I'm not asking for a solution, but an approach. How do I prove this kind of question? I have tried to arrange it so that it 
is $x + y$ = ....
But I still get nothing, nothing intuitive at least. What is a way to tackle this problem?
 [/INST] Hint:
By expanding we have 
\begin{align*}
(x+y)^2&=(x+3)(y-3)\\
\iff x^2+2xy+y^2&=xy-3x+3y-9\\
\iff x^2+xy+y^2+3x-3y+9&=0\\
\iff \tfrac12(x+y)^2+\tfrac12(x+3)^2+\tfrac12(y-3)^2&=0
\end{align*}
So we must have $$x+y=x+3=y-3=0$$
</s>