Results 1 to 4 of 4

Math Help - X, Y et Z.

  1. #1
    Junior Member phgao's Avatar
    Joined
    May 2005
    Posts
    39

    X, Y et Z.

    X, Y and Z are positive integers such that X^2 + 2Y^2 + 3Z^2 = 1417.
    What is the value of X + Y + Z? Find all possible solutions.

    I think this needs a program/ excel but I have no idea how to set somehting out. Help would be appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,829
    Thanks
    123
    I add a Delphi-procedure, which calculates the possible solutions in the form (x, y, z) if you use only positive integers.


    procedure TForm1.Button2Click(Sender: TObject);
    var x,y,z:integer;
    begin
    for x:= 1 to 50 do
    for y:= 1 to 45 do
    for z := 1 to 40 do
    begin
    if (x*x+2*y*y+3*z*z=1417) then
    begin
    form1.memo1.lines.add(inttostr(x));
    form1.memo2.lines.add(inttostr(y));
    form1.memo3.lines.add(inttostr(z));
    end;
    end;
    end;


    (1, 18, 16)
    (10, 15, 17)
    (19, 12, 16)
    (34, 3, 9)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member phgao's Avatar
    Joined
    May 2005
    Posts
    39
    Wow, i'll have to do some more research to understand fully your explanation. Thanks!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,829
    Thanks
    123
    Hi, phgao,
    I did a little further investigation about your equation (it's a very interesting one!): If you use real numbers, the value for x runs from - 38 < x < 38 (because of the squares in your equation the lowest value could only be zero. So when y^2 and z^2 are zeros, the highest value for the x is approximately sqrt(1417)); -27 < y < 27 and -22 < z 22 .
    You'll get an infinit number of triples which could be considered as coordinates in 3-d-graph. All points create the surface of an ellipsoid.
    I've tried to attach the above mentioned graph but I'm not quite sure that you got the image because at the preview I cann't detect any image at all: tri_reell.gif
    Attached Thumbnails Attached Thumbnails X, Y et Z.-tri_reell.gif  
    Follow Math Help Forum on Facebook and Google+


/mathhelpforum @mathhelpforum