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Math Help - Algebra

  1. #1
    Newbie
    Joined
    May 2007
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    Algebra

    Q= If x + y = a

    and x^2 + y^2 = b^2

    find an expression for ( x^2 - y^2)^2 in terms of a and b

    cheers for the help
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  2. #2
    Senior Member JaneBennet's Avatar
    Joined
    Dec 2007
    Posts
    293
    \begin{array}{lrcl}<br />
{} & x+y &=& a\\\\<br />
\Rightarrow & x^2+2xy+y^2 &=& a^2\\\\<br />
\Rightarrow & 2xy &=& a^2-b^2\\\\<br />
\Rightarrow & 4x^2y^2 &=& (a^2-b^2)^2<br />
\end{array}

    Now use the formula (x^2-y^2)^2=(x^2+y^2)^2-4x^2y^2 to finish off.
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