Question

Найдите значение выражения:

$(frac{1}{m}-frac{1}{n})*frac{m^2n^2}{m^2-n^2}$

при m=2-$sqrt{2}$, n=2+$sqrt{2}$

Answer 1

(frac{1}{m}-frac{1}{n})*frac{m^2n^2}{m^2-n^2}=frac{n-m}{mn}*frac{m^2n^2}{(m-n)(m+n)}=frac{-mn}{m+n}

 

 

 

$frac{-(2-sqrt{2})(2+sqrt{2})}{2-sqrt{2}+2+sqrt{2}}=frac{-(4-2)}{2+2}=frac{-2}{4}=-frac{1}{2}$