Question

Determine o valor da equação 15 + 2 Cx,2 = 45

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação:

$\mathsf{15 + 2\:C_{x,2} = 45}$

$\mathsf{2\:C_{x,2} = 45 - 15}$

$\mathsf{2\:C_{x,2} = 30}$

$\mathsf{\:C_{x,2} = 15}$

$\mathsf{\:\dfrac{x!}{2!.(x -2)!} = 15}$

$\mathsf{\:\dfrac{x.(x-1).(x-2)!}{2!.(x -2)!} = 15}$

$\mathsf{x.(x-1) = 30}$

$\mathsf{x^2 - x = 30}$

$\mathsf{x^2 - x - 30 = 0}$

$\mathsf{\Delta = b^2 - 4.a.c}$

$\mathsf{\Delta = (-1)^2 - 4.1.(-30)}$

$\mathsf{\Delta = 1 + 120}$

$\mathsf{\Delta = 121}$

$\mathsf{x = \dfrac{-b \pm \sqrt{\Delta}}{2a} = \dfrac{1 \pm \sqrt{121}}{2} \rightarrow \begin{cases}\mathsf{x' = \dfrac{1 + 11}{2} = \dfrac{12}{2} = 6}\\\\\mathsf{x'' = \dfrac{1 - 11}{2} = \dfrac{-10}{2} = -5}\end{cases}}$

$\boxed{\boxed{\mathsf{S = \{6\}}}}$