[tex]\displaystyle\bf\\Sa~se~rezolve~ecuatia:\\\\C_n^2=28,~~n\in N,~~n\geq 2\\\\Explicatii:\\\\C_n^2~~se~citeste:~(Combinari~de~n~luate~cate~2)\\\\A_n^2~~se~citeste:~(Aranjamente~de~n~luate~cate~2)\\\\P_n~~se~citeste:~(Permutari~de~n)\\\\n!~~se~citeste:~(n~factorial)\\\\Capitolul~dim~matematica~in~care~se~studiaza\\se~numeste~"COMBINATORICA"\\\\Rezolvare:\\\\C_n^2=28\\\\\frac{A_n^2}{P_2}=28\\\\\frac{n(n-1)}{1\times2}=28\\\\\frac{n^2-n}{2}=28\\\\ n^2-n=28\times2\\\\ n^2-n=56[/tex]
.
[tex]\displaystyle\bf\\n^2-n-56=0\\\\Rezolvam~ecuatia~de~gradul~2.\\\\n_{12}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{1\pm\sqrt{1+4\times56}}{2}=\frac{1\pm\sqrt{225}}{2}=\frac{1\pm15}{2}.\\\\n1=\frac{1+15}{2}=\frac{16}{2}=8\\\\n2=\frac{1-15}{2}=\frac{-14}{2}=-7\notin N~~(Solutie~respinsa)\\\\\implies~\boxed{\bf n=8~solutie~unica}[/tex]
