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Math Help - Take integers a,b,c,d. Show that...

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    Take integers a,b,c,d. Show that...

    Take integers a,b,c,d. Show that (a+b*sqrt(2))/(c+d*sqrt(2)) = (ac-2bd)/(c^2-2d^2) + ((bc-ad)*sqrt(2))/(c^2-2d^2). Then choose integers s and t differing from those terms by at most + or - 1/2. Show that the norm of the difference between the expression above and s+t*sqrt(2) has norm less than 1.

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    MHF Contributor Bruno J.'s Avatar
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    Begin by using the fact that (c+d\sqrt{2})^{-1}=\frac{c-d\sqrt{2}}{c^2-2d^2}.
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