Question 176
Let $a$ and $b$ be positive reals satisfying
$$
\begin{cases} a^2 = 2 + b \\ b^3 = 3 - a \end{cases}.
$$
Find all positive integer $n$ such that the equation $x^n + a x + b = 0$ has no real solutions.
$$
\begin{cases} a^2 = 2 + b \\ b^3 = 3 - a \end{cases}.
$$
Find all positive integer $n$ such that the equation $x^n + a x + b = 0$ has no real solutions.