Results 1 to 4 of 4

Math Help - d2 = a2 + b2 + c2

  1. #1
    Senior Member pacman's Avatar
    Joined
    Jul 2009
    Posts
    448

    d2 = a2 + b2 + c2

    If d^2 = a^2 + b^2 + c^2 , then show that (a + b + c + 2d)^2 = (a + b + d)^2 + (a + c + d)^2 + (b + c + d)^2
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2008
    From
    West Malaysia
    Posts
    1,261
    Quote Originally Posted by pacman View Post
    If d^2 = a^2 + b^2 + c^2 , then show that (a + b + c + 2d)^2 = (a + b + d)^2 + (a + c + d)^2 + (b + c + d)^2
    HI

    Let a+b+c+d=k ---1

    (a + b + d)^2 + (a + c + d)^2 + (b + c + d)^2

    =(k-c)^2+(k-b)^2+(k-a)^2

    =k^2-2kc+c^2+b^2-2kb+b^2+k^2-2ka+a^2

    =3k^2-2k(k-d)+d^2

    =k^2+2kd+d^2

    =(k+d)^2

    then from 1

    =(a+b+c+d+d)^2

     <br />
=(a+b+c+2d)^2<br />

    Hence shown
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member pacman's Avatar
    Joined
    Jul 2009
    Posts
    448
    mathaddict, i like your substitution method, by letting . Better than my manual expansion of the squared terms and cancelations . . . .
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Sep 2008
    From
    West Malaysia
    Posts
    1,261
    Quote Originally Posted by pacman View Post
    mathaddict, i like your substitution method, by letting . Better than my manual expansion of the squared terms and cancelations . . . .
    yeah , the working can be very tedious if you were to expand the whole thing .
    Follow Math Help Forum on Facebook and Google+


/mathhelpforum @mathhelpforum