Question 6
(CZS 4) Find the real values of $p$ for which the equation
$$\sqrt{2p+1-x^2}+\sqrt{3x+p+4}=\sqrt{x^2+9x+3p+9}$$
in $x$ has exactly two real distinct roots ($\sqrt t$ means the positive square root of $t$).
$$\sqrt{2p+1-x^2}+\sqrt{3x+p+4}=\sqrt{x^2+9x+3p+9}$$
in $x$ has exactly two real distinct roots ($\sqrt t$ means the positive square root of $t$).