Question

Упростить выражения 80 баллов

Answer 1

а) (с+1/с)²-2=с²+2*с*1/с+(1/с)²-2=с²+2+1/с²-2=с²+1/с²

б)(m-2/m)²-(m+2/m)²=(m-2/m-(m+2/m))(m-2/m+m+2/m)=
   (m-2/m-m-2/m))2m= -4/m*2m=-8

в)
$( frac{x}{y} + frac{y} {x})^2-( frac{x^2}{y^2} + frac{y^2} {x^2})=( frac{x}{y})^2+2* frac{x}{y} *frac{y} {x} + (frac{y} {x})^2- frac{x^2}{y^2} - frac{y^2} {x^2}= \ = frac{x^2}{y^2}+2* frac{xy}{yx} + frac{y^2} {x^2}- frac{x^2}{y^2} - frac{y^2} {x^2}=2* frac{xy}{yx} =2$

г)
$(a+ frac{a+1}{a})^2- (a- frac{a+1}{a})^2= \ (a+ frac{a+1}{a}- (a- frac{a+1}{a}))*(a+ frac{a+1}{a}+ (a- frac{a+1}{a}))= \ (a+ frac{a+1}{a}- a+ frac{a+1}{a})*(a+ frac{a+1}{a}+ a- frac{a+1}{a})= \ ( frac{a+1}{a}+ frac{a+1}{a})*(a+ a)= frac{2(a+1)}{a}*2a=4(a+1)=4a+4$