Question

Найдите значение выражения
(m-n +1) ^2 - (m-1+n) ^2 /4m ×(n+1) при m=25/13, n= корень из 2

Answer 1

$\frac{(m-n+1)^2-(m-1+n)^2}{4m}*(n+1)=\frac{(m+1)^2-2(m+1)n+n^2-(m-1+n)^2}{4m}(n+1)=$

=$=\frac{(-2n-2mn+1+2m+m^2+n^2-1+2m-m^2+2n-2mn-n^2)(n+1)}{4m}=$

$=\frac{(4m-4mn)(n+1)}{4m}=\frac{4m(1-n)(n+1)}{4m}=(1-n)(n+1)=$

$=(1-\sqrt{2})(\sqrt{2}+1)=1+\sqrt{2}-\sqrt{2}-2=-1$