Question 1206697

 
{{{(n/(n+1))^2 + (n/(n-1))^2 = 12}}}

 {{{n^2/(n+1)^2 + n^2/(n-1)^2 = 12}}}


{{{(n^2(n-1)^2) + n^2(n+1)^2)/((n+1)^2*(n-1)^2) = 12}}}


{{{n^2(n-1)^2) + n^2(n+1)^2 = 12((n+1)^2*(n-1)^2)}}}


{{{2 n^4 +2n^2  = 12n^4 - 24n^2 + 12}}}...divide by {{{2}}}


{{{n^4 +n^2  = 6n^4 - 12n^2 + 6}}}


{{{6n^4 - 12n^2 + 6-n^4 -n^2 =0}}}


{{{5n^4 - 13n^2 + 6  =0}}}


{{{5n^4 - 10n^2-3n^2 + 6  =0}}}


{{{(5n^4 - 10n^2)-(3n^2 - 6 ) =0}}}


{{{5n^2(n^2 - 2)-3(n^2 - 2 ) =0}}}


{{{(n^2 - 2) (5n^2 - 3) = 0}}}


if {{{(n^2 - 2)  = 0}}}=> {{{n^2=2}}} => {{{n=sqrt(2)}}} or {{{n=-sqrt(2)}}}

if {{{(5n^2 - 3) = 0}}}=> {{{5n^2=3 }}}=> {{{n=sqrt(3/5)}}} or {{{n=-sqrt(3/5)}}}


solutions:

{{{n=sqrt(2)}}} 

{{{n=-sqrt(2)}}}

{{{n=sqrt(3/5)}}}

{{{n=-sqrt(3/5)}}}