If for the real numbers $a,b(a\ne b)$ it is true that $a^2=2b+15$ and $b^2=2a+15$, then what is the value of the product $ab$? If for the real numbers $a,b(a\ne b)$ it is true that $a^2=2b+15$ and $b^2=2a+15$, then what is the value of the product $ab$?
I tried to solve it as follows:
I state that $p=ab$
$p^2=(2b+15)(2a+15)$
$p^2=4ab+30(a+b)+225$
$p^2=4p+30(a+b)+225$
and this is where I got stuck. I don't know how to get over this hurdle. could you please explain to me how to solve the question?

$a^2=2b+15$ and $b^2=2a+15$
Subtracting, $a^2-b^2 = -2(a-b)$. As $a \ne b$,
$a+b = - 2$
Also adding both equations, $a^2+b^2 = 2(a+b)+30 = 26$
$(a+b)^2 = a^2+b^2+2ab \implies 4 = 26 + 2ab$
$ab = -11$
