Question 10
Determine the smallest constant $C$ such that the inequality
$$
(X + Y)^2 (X^2 + Y^2 + C) + (1 - XY)^2 \geq 0
$$
holds for all real numbers $X$ and $Y$.
For which values of $X$ and $Y$ does equality hold for this smallest constant $C$?
$$
(X + Y)^2 (X^2 + Y^2 + C) + (1 - XY)^2 \geq 0
$$
holds for all real numbers $X$ and $Y$.
For which values of $X$ and $Y$ does equality hold for this smallest constant $C$?