Question

Find the number of solutions for $\left[x\right]=\left\{x\right\}$. Where $\left[x\right],\left\{x\right\}$ represents greatest integer and fractional part of x.

___

Answer 1

As, $\left[x\right]=\left\{x\right\}$

We will plot $y=\left[x\right]$, $y=\left\{x\right\}$ and find point of intersection.

Here,the only point of intersection is x=0,

$\therefore$ only one solutions.