Resposta:
[tex]\textsf{Leia abaixo}[/tex]
Explicação passo a passo:
[tex]\mathsf{C_{n,2} + C_{n+1,n - 1} = 25}[/tex]
[tex]\mathsf{\dfrac{n!}{2!.(n - 2)!} + \dfrac{(n + 1)!}{(n - 1)!.2!} = 25}[/tex]
[tex]\mathsf{\dfrac{n.(n - 1).(n - 2)!}{2!.(n - 2)!} + \dfrac{(n + 1).n.(n - 1)!}{(n - 1)!.2!} = 25}[/tex]
[tex]\mathsf{n.(n - 1) + n.(n + 1) = 25}[/tex]
[tex]\mathsf{n^2 - n + n^2 + n = 25}[/tex]
[tex]\mathsf{2n^2 = 25}[/tex]
[tex]\mathsf{n = \dfrac{5}{\sqrt{2}}}[/tex]
[tex]\boxed{\boxed{\mathsf{n = \dfrac{5\sqrt{2}}{2}}}}[/tex]
