1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Solve this inequality

  1. Apr 22, 2013 #1

    utkarshakash

    User Avatar
    Gold Member

    1. The problem statement, all variables and given/known data
    [itex]x^2 \geq [x]^2[/itex]

    [] denotes Greatest Integer Function
    {} denotes Fractional Part
    2. Relevant equations

    3. 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]
     
  2. jcsd
  3. Apr 22, 2013 #2

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    How do you go from the above step to the next step.

    (It does look valid, but an explanation seems to be in order.)

     
  4. Apr 23, 2013 #3

    utkarshakash

    User Avatar
    Gold Member

    Ah! I made a silly mistake there. Actually it should be like this

    [itex]x \in \left( -∞, -[x] \right] U \left[ [x],∞ \right) [/itex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Solve this inequality
  1. Solve inequality (Replies: 12)

  2. Solving Inequalities (Replies: 3)

  3. Solve the inequality (Replies: 9)

  4. Solve inequality (Replies: 1)

  5. Solving an inequality (Replies: 14)

Loading...