[tex]n \bullet \frac{1}{n} = 2(n+\frac{1}{n}) - \frac{n*\frac{1}{n} }{2} = 2\frac{n^2+1}{n} - \frac{1}{2}[/tex]
[tex]\frac{2n^2+2}{n} -\frac{1}{2} =\frac{9}{2} \\\frac{2n^2+2}{n} = \frac{10}{2}\\\\4n^2+4=10n\\4n^2-10n+4=0\\2n^2-5n+2=0\\\Delta = 25-16=9\\ \\n = \frac{5 \pm \sqrt{9}}{4} = \frac{5 \pm 3}{4}[/tex]
[tex]n_1 = 8\\n_2 = \frac{1}{2}[/tex]
Dintre aceste doua solutii doar 8 este numar natural. Deci raspunsul este n=8
