Results 1 to 7 of 7

Math Help - flloor and ceiling question

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    11

    flloor and ceiling question

    Hi, I think the answer of this question x=   \sqrt{1/2}. But I am not sure for this answer. What do you think about for this problem ?
    Attached Thumbnails Attached Thumbnails flloor and ceiling question-question3.jpg  
    Last edited by Plato; November 27th 2009 at 08:21 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,966
    Thanks
    1785
    Awards
    1
    Quote Originally Posted by isiksoy7 View Post
    Hi, I think the answer of this question x=   \sqrt{1/2}. But I am not sure for this answer. What do you think about for this problem ?
    That is correct.
    There is a second answer.
    Last edited by Plato; November 27th 2009 at 08:38 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2009
    Posts
    11
    Quote Originally Posted by Plato View Post
    That is correct.
    There is a second answer.
    What is the second answer ?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,966
    Thanks
    1785
    Awards
    1
    Quote Originally Posted by isiksoy7 View Post
    What is the second answer ?
    Graph the function x^2  - \left\lfloor x \right\rfloor from 0 to 3.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor chisigma's Avatar
    Joined
    Mar 2009
    From
    near Piacenza (Italy)
    Posts
    2,162
    Thanks
    5
    ... a very easy alternative to find the solutions of the equation...

    x^{2} - \lfloor {x} \rfloor = \frac{1}{2} (1)

    ... is to set \lfloor {x} \rfloor = k with k integer and verify if the solution of the 'standard' second order equation...

    x^{2} - k =\frac{1}{2} (2)

    ... is also solution of (1)...

    Kind regards

    \chi \sigma
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Nov 2009
    Posts
    11
    Quote Originally Posted by chisigma View Post
    ... a very easy alternative to find the solutions of the equation...

    x^{2} - \lfloor {x} \rfloor = \frac{1}{2} (1)

    ... is to set \lfloor {x} \rfloor = k with k integer and verify if the solution of the 'standard' second order equation...

    x^{2} - k =\frac{1}{2} (2)

    ... is also solution of (1)...

    Kind regards

    \chi \sigma
    if I request , you can explain more please I am young at this topic and hard for me.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor chisigma's Avatar
    Joined
    Mar 2009
    From
    near Piacenza (Italy)
    Posts
    2,162
    Thanks
    5
    All right!... it is self evident that \lfloor {x} \rfloor is an integer that we can indicate with k. Because x^{2} \ge 0 and \frac{1}{2} >0 and is...

    x^{2} - \lfloor {x} \rfloor = x^{2} - k = \frac{1}{2} (1)

    ... we have to suppose that is k \ge 0. Now we proceed 'step by step' to verify with increasing value of k starting from 0...

    k=0 \rightarrow x^{2} = \frac{1}{2} \rightarrow x= \sqrt{\frac{1}{2}} (2)

    and because \lfloor {x} \rfloor =0 =k , x= \sqrt{\frac{1}{2}} is solution of (1)...

    k=1 \rightarrow x^{2} = \frac{3}{2} \rightarrow x= \sqrt{\frac{3}{2}} (3)

    and because \lfloor {x} \rfloor = 1 =k , x= \sqrt{\frac{3}{2}} is also solution of (1)...

    For k>1 there are no more solution , so that the (1) has two solutions... like a 'standard' second order equation ...

    Kind regards

    \chi \sigma
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Ceiling and Floor
    Posted in the Number Theory Forum
    Replies: 8
    Last Post: November 14th 2010, 06:47 PM
  2. ceiling and floor functions
    Posted in the LaTeX Help Forum
    Replies: 1
    Last Post: October 21st 2010, 05:24 PM
  3. [SOLVED] Ceiling Functions
    Posted in the Number Theory Forum
    Replies: 8
    Last Post: May 18th 2010, 12:56 PM
  4. Floor and Ceiling stuff.
    Posted in the Calculus Forum
    Replies: 5
    Last Post: October 20th 2009, 04:42 PM
  5. Help with floor and ceiling functions
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: August 9th 2009, 11:30 PM

Search Tags


/mathhelpforum @mathhelpforum