Question

o multime cu n elemente are 10 submultimi cu cate 2 elemente. Cate elemente are multimea?​

Answer 1

 

$\displaystyle\bf\\\textbf{Numarul de submultimi a unei multimi cu n elemente = }C_n^2\\\\C_n^2=10\\\\\frac{n(n-1)}{1\times2}=10\\\\\frac{n(n-1)}{2}=10\\\\n(n-1)=10\times2\\\\n(n-1)=20\\\\n~si~(n-1)~sunt~numere~consecutive.\\\\\textbf{Descompunem numarul 20 in produs de 2 numere consecutive.}\\\\n(n-1)=5\times4\\\\\implies~~\boxed{\bf~n=5~elemente~are~multimea}$