Find all non-integers $x$ such that $x+\frac{13}{x}=[x]+\frac{13}{[x]} . $where$[x]$ mean the greatest integer $n$ , where $n\leq x.$
Problem
Source: China Xian , 27 Jul --3 Aug
Tags: algebra proposed, algebra, floor function, Solve equation
Source: China Xian , 27 Jul --3 Aug
Tags: algebra proposed, algebra, floor function, Solve equation
Find all non-integers $x$ such that $x+\frac{13}{x}=[x]+\frac{13}{[x]} . $where$[x]$ mean the greatest integer $n$ , where $n\leq x.$