Question

C n,2=6 preciso da resolução !

Answer 1

$C_{n,2} = 6 \\\\ \frac{n!}{2! \cdot (n-2)!} = 6 \\\\ \text{pela sequencia, saimos do n! para chegar no (n-2)!}{} \\\\ \frac{n \cdot (n-1) \cdot (n-2)!}{2 \cdot (n-2)!} = 6 \\\\ \frac{n \cdot (n-1) \cdot (n\not{-2})!}{2 \cdot (n\not{-2})!} = 6 \\\\ \frac{n \cdot (n-1)}{2} = 6 \\\\ n \cdot (n-1) = 2 \cdot 6 \\\\ n \cdot (n-1) =12 \\\\ n^{2}-n = 12 \\\\ n^{2}-n-12 = 0$

$\Delta = b^{2}-4 \cdot a \cdot c \\\\ \Delta = (-1)^{2} - 4 \cdot (1) \cdot (-12) \\\\ \Delta = 1+48 \\\\ \Delta = 49 \\\\\\ x = \frac{-b \pm \sqrt{\Delta}}{2a} \\\\ x = \frac{-(-1) \pm \sqrt{49}}{2 \cdot 1} \\\\ x = \frac{1 \pm 7}{2} \\\\\\ x' = \frac{1 + 7}{2} = \frac{8}{2} = \boxed{4} \\\\ x'' =\frac{1 - 7}{2} = \frac{-6}{2} = \boxed{-3}$


Negativo não entra, portanto:

$\boxed{\boxed{S = \{4\}}}$