- #1

utkarshakash

Gold Member

- 855

- 13

## Homework Statement

[itex]x^2 \geq [x]^2[/itex]

[] denotes Greatest Integer Function

{} denotes Fractional Part

## Homework Equations

## The Attempt at a Solution

[itex] x^2-[x]^2 \geq 0 \\

(x+[x])(x-[x]) \geq 0 \\

-[x] \leq x \leq [x] \\

[/itex]

Considering left inequality

[itex]

x \geq -[x] \\

\left\{x\right\} \geq -2[x]

[/itex]