Results 1 to 4 of 4

Math Help - A^2=B^2, C^2=D^2......does (A+C)^2=(B+D)^2?

  1. #1
    Newbie
    Joined
    Sep 2008
    Posts
    16

    A^2=B^2, C^2=D^2......does (A+C)^2=(B+D)^2?

    Given
    A^2=B^2, C^2=D^2

    ......does (A+C)^2=(B+D)^2?

    I got down to this

    AC=BD

    I then divived both sides by "A"

    C=BD/A

    My proof goes as following....

    It is possible that B=A.....eg A=6....B=6.....A^2=B^2.......36=36

    So if this is possible. this equation breaks down to

    C=D.... However it is clear that C is not always equal to D

    Can anyone recommend a better proof?

    Thankyou
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Aug 2009
    From
    Israel
    Posts
    976
    What about A=B=1, C=1, D=-1?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2008
    Posts
    16
    extra note:

    i ended up with

    AC=BD

    +-A/+-B=+-D/C
    +-1=+-1

    Which is not always TRUE.... all i have to do is show one case where it is not true.....

    Defunkt. For A=B=1,C=-1,D=1

    it becomes

    1=1/-1....which is false. Do you think this proof is ok?

    All im proving is that it doesnt work for all numbers of A and B... shouldnt all
    i have to show is one FALSE? thanks for the input
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Aug 2009
    From
    Israel
    Posts
    976
    Quote Originally Posted by sebko View Post
    extra note:

    i ended up with

    AC=BD

    +-A/+-B=+-D/C
    +-1=+-1

    Which is not always TRUE.... all i have to do is show one case where it is not true.....

    Defunkt. For A=B=1,C=-1,D=1

    it becomes

    1=1/-1....which is false. Do you think this proof is ok?

    All im proving is that it doesnt work for all numbers of A and B... shouldnt all
    i have to show is one FALSE? thanks for the input
    That is correct! (It is false because A^2 = B^2 = 1 \ , \ C^2 = D^2 = 1 but (A+C)^2 = 2^2 = 4 \neq 0 = (1 + (-1))^2 = (B + D)^2)
    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum