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Math Help - algebra problem

  1. #1
    Junior Member
    Joined
    Dec 2008
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    68

    Exclamation algebra problem

    help me.....im stupid.....

    redical x^2 - y^2 = 6

    the answer is x=10 & y=8 .......................but how can i get it..............thnx
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  2. #2
    MHF Contributor
    Joined
    Nov 2008
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    France
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    1,458
    Hi

    I suppose that x and y are integers
    \sqrt{x^2-y^2} = 6
    x^2-y^2 = 36
    (x-y)(x+y) = 36 = 2^2 \cdot 3^2

    (x-y) being smaller than (x+y) the possibilities for ((x-y),(x+y)) are (1,36) ; (2,18) ; (3,12) ; (4;9) ; (6;6)
    Their sum must be even because (x-y)+(x+y)=2x
    Remain 2 possibilities
    (2,18) => x=10 and y=8
    (6,6) => x=6 and y=0
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