Results 1 to 3 of 3

Math Help - Help with proving (ab'-a'b)^2+4(ah'-a'h)(bh'-b'h) is square of a rational number

  1. #1
    Newbie
    Joined
    May 2012
    From
    Chennai
    Posts
    2

    Help with proving (ab'-a'b)^2+4(ah'-a'h)(bh'-b'h) is square of a rational number

    Given:
    a(x^2)+2hxy+b(y^2)=1
    a'(x^2)+2h'xy+b'(y^2)=1

    for x,y in R
    where a,b,h,a',b',h' are rational.

    Prove that:
    i)(h-h')^2-(a-a')(b-b')
    ii)(ab'-a'b)^2+4(ah'-a'h)(bh'-b'h)

    are both squares of rational numbers.

    I proved i) easily by simply subtracting the two equations and getting a quadratic in (x/y). I have been trying to prove ii) but don't know where to begin. If some one could give me a nudge in the right direction it will be very helpful.

    Thanks
    Last edited by harihar90; May 6th 2012 at 03:43 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Apr 2012
    From
    london
    Posts
    10

    Re: Help with proving (ab'-a'b)^2+4(ah'-a'h)(bh'-b'h) is square of a rational number

    Hi, please don't leave out conditions that is obvious to you, but not obvious to others.

    Eg, I guess the given x,y equations are valid for any x,y in R, right? what is h? A constant in R?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2012
    From
    Chennai
    Posts
    2

    Re: Help with proving (ab'-a'b)^2+4(ah'-a'h)(bh'-b'h) is square of a rational number

    hi. sorry. Edited the post to answer your questions.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Is this a rational number?
    Posted in the Algebra Forum
    Replies: 7
    Last Post: October 6th 2011, 08:40 AM
  2. Replies: 4
    Last Post: April 28th 2011, 06:20 AM
  3. proving rational number inequalities
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: April 22nd 2011, 04:48 PM
  4. Proving a rational number
    Posted in the Differential Geometry Forum
    Replies: 5
    Last Post: February 11th 2010, 11:52 AM
  5. Replies: 5
    Last Post: October 7th 2008, 12:55 PM

Search Tags


/mathhelpforum @mathhelpforum