If $ x^2+1/x^2=38$ find$x-1/x$

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If $x^2+1/x^2=38$ find $x-1/x$

A10

Answer:

$(x-1/x)^2=x^2+2-1/x^2$

$(x-1/x)^2=x^2+1/x^2-2=38-2=36$

$x-1/x=\sqrt{36}=6$

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