Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Advance Math

  1. Mar 24, 2009 #1
    Hi,

    Anybody can help me prove this? Thanks...

    If x<0 and y<0 and x<y, then [y][/2] < [x][/2]
     
  2. jcsd
  3. Mar 24, 2009 #2

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    Hi, welcome to PF.

    What does the brackets notation mean?
    What is [y][/2] ?
     
  4. Mar 27, 2009 #3
    That is y squared is greater than x squared
     
  5. Mar 27, 2009 #4
    You seem to have said that y squared is LESS than x squared in your original post.
     
  6. Mar 28, 2009 #5

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    That's correct. Because x<y<0.

    This might be the kind of thing you want to do in parts. For example, prove that x2 = (-x)2 so you can switch this to looking at positive numbers
     
  7. Mar 28, 2009 #6

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    You mean, "if x< 0, y< 0 and x< y, then y2< x2". If you don't want to use HTML tags or LaTex, the y^2< x^2 is the best way to show an exponent.

    It is easy to show that if 0< a< b, then a2< b2. Here, since x< y< 0, 0< -y< -x so (-y)2< (-x)2 which, because (-x)2= x2 and (-y)2= y2, leads to your result.
     
  8. Mar 29, 2009 #7
    edit:
    Use
    If a < b, then c * b < c * a if and only if c < 0.
    Spoiler :
    We have x < 0, y < 0 and x < y. Then x * y < x * x, because x < 0. Similarly, y * y < y * x, because y < 0. So,
    y^2 = y * y < y * x = x * y < x * x = x^2,
    giving y^2 < x^2.

    o:)
     
    Last edited: Mar 29, 2009
  9. Mar 29, 2009 #8

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    See, if you'll wait long enough with replying, we'll solve the entire question for you :smile:
     
  10. Apr 6, 2009 #9

    We have x<y and x<0 and y<0 ,so if we multiply x<y by x<0 we get:

    [tex]x^2>xy[/tex].................................................................1

    and if we multiply x<y by y<0 we get:

    [tex]xy> y^2[/tex]..................................................................2

    And from (1) and (2) we have : [tex] x^2> y^2[/tex],using the fact .

    If A>B AND B>C ,then A>C
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook