Question

розвязати рівняння терміново

Answer 1

$Sdisplaystyle bigg(frac{1}{x(n+1)} +frac{1}{x(n-1)}-frac{1}{x}bigg)=0\ S=0;~~ x in (-infty;0)cup(0;+infty);~~~ n in (-infty;-1)cup(-1;1)cup(1;+infty) \ \if~~ Sne 0~~ and~~ xin (-infty;0)cup(0;+infty)~~ than \ \ frac{1}{x(n+1)} +frac{1}{x(n-1)}-frac{1}{x}=0\ \ frac{n-1+n+1-(n-1)(n+1)}{x(n+1)(n-1)} =0\ \ 2n-n^2+1=0\ n^2-2n-1=0\ D=8\ n_{1,2}=1pmsqrt{2}$

В качестве x можно взять любое число, кроме 0.

Answer 2

S не обязательно 0

Answer 3

$frac{S}{x} (frac{1}{n+1} +frac{1}{n-1} ) = frac{S}{x} \ 1)S = 0; x in R/{0}; n in R/{-1; 1}\ 2) Sin R/{0}; x in R/{0};\ frac{1}{n+1}+frac{1}{n-1} =1\ frac{2n}{n^2-1} =1\ n^2-1=2n\ n^2-2n-1=0\ D=4+4=8\ n_1=frac{2-2sqrt{2}}{2} =1-sqrt{2}\ n_2=1+sqrt{2}$