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- Feb 14, 2012

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- Feb 14, 2012

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$c$ and $d$ satisfy the equation $(x^2-4)^2 = 5+x$, or $x^4 - 8x^2 - x + 11 = 0\quad(**).$

But if $x$ satisfies (**) then $-x$ satisfies (*). So the roots of (*) are $a,b,-c,-d.$ Thus $abcd$ is the product of the roots of (*), namely 11.

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Well done,

$c$ and $d$ satisfy the equation $(x^2-4)^2 = 5+x$, or $x^4 - 8x^2 - x + 11 = 0\quad(**).$

But if $x$ satisfies (**) then $-x$ satisfies (*). So the roots of (*) are $a,b,-c,-d.$ Thus $abcd$ is the product of the roots of (*), namely 11.