Results 1 to 4 of 4

Math Help - demonstration - help

  1. #1
    Newbie
    Joined
    Aug 2007
    Posts
    3

    Post demonstration - help

    Demonstrate if x,y,z are > or = than 0.

    (x+y)(y+z)(z+x) => 8xyz




    "=>" is grater or equal
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,111
    Thanks
    2
    You CAN just beat the tar out of it...

    1) Multiply out the LHS.
    2) Subtract the 2xyz
    3) Divide by xyz
    4) Rearrange so that reciprocals are grouped together.
    5) Ponder the reciprocal pairs.
    6) Prove that any reciprocal pair >= 2

    Hint:

    f(A) = A + 1/A

    What can you tell of that? Maybe a graph would be helpful?

    Nothing like a little algebra practrice.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    13
    Quote Originally Posted by voidstuff View Post
    Demonstrate if x,y,z are > or = than 0.

    (x+y)(y+z)(z+x) => 8xyz




    "=>" is grater or equal
    This is a well-known inequality.

    We know that

    x,y,z\ge0\implies\begin{cases}x+y&\ge2\sqrt{xy}\\y  +z&\ge2\sqrt{yz}\\x+z&\ge2\sqrt{xz}\end{cases}

    Multiply this inequalities to get the desired.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Aug 2007
    Posts
    3
    thanks a lot... I was trying to solve it with a similar inecuation:

    i was using
    x,y,z\ge0\implies\begin{cases}x^2+y^2&\ge2xy\\y^2+  z^2&\ge2yz\\x^2+z^2&\ge2xz\end{cases}
    which was the same thing you proposed but adding 2xy on both sides.

    gracias amigo chileno xD
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Big O, little o demonstration
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: March 16th 2011, 08:46 PM
  2. Demonstration, please help.
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: April 24th 2010, 08:05 AM
  3. Demonstration
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: June 26th 2009, 12:32 AM
  4. Trigonometry demonstration
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: June 19th 2009, 11:56 PM
  5. Demonstration
    Posted in the Calculus Forum
    Replies: 0
    Last Post: June 8th 2009, 01:42 PM

Search Tags


/mathhelpforum @mathhelpforum