For a real number $a$, $[a]$ denotes the largest integer not exceeding $a$. Find all positive real numbers $x$ satisfying the equation $$x\cdot [x]+2022=[x^2]$$
Source: 2022 Turkey JBMO TST P2
Tags: algebra, floor function
For a real number $a$, $[a]$ denotes the largest integer not exceeding $a$. Find all positive real numbers $x$ satisfying the equation $$x\cdot [x]+2022=[x^2]$$