Question 86
Find all real numbers $x$ such that
$$
\left\lfloor \frac{x^2 + 1}{x + 2} \right\rfloor + \left\lfloor \frac{x - 1}{2} \right\rfloor = \frac{x(3x + 1)}{2(x + 2)}
$$
For a real number $t$, $\lfloor t \rfloor$ denotes the largest integer not greater than $t$. For example, if $t = 3.14$, then $\lfloor t \rfloor = 3$.
$$
\left\lfloor \frac{x^2 + 1}{x + 2} \right\rfloor + \left\lfloor \frac{x - 1}{2} \right\rfloor = \frac{x(3x + 1)}{2(x + 2)}
$$
For a real number $t$, $\lfloor t \rfloor$ denotes the largest integer not greater than $t$. For example, if $t = 3.14$, then $\lfloor t \rfloor = 3$.