Question

(n + 3) ! = 20
(n+1)!​

Answer 1

Resposta:

Explicação passo a passo:

(n + 3) ! = 20 (n+1)!​

$(n + 3)! = 20(n + 1)!\\\\\frac{(n + 3)!}{(n + 1)!} =20\\\\\frac{(n + 3)(n + 2)(n + 1)!}{(n + 1)!} =20\\\\(n + 3)(n + 2)=20$

$n^2+2n+3n+6=20\\\\n^2+5n+6-20=0\\\\n^2+5n-14=0\\\\\Delta = 5^2 - 4 * 1 * (-14)\\\\\Delta = 25 + 56 = 81$

$x'=\frac{-5+\sqrt{81} }{2} \\\\x'=\frac{-5+9 }{2} = \frac{4}{2} \\\\x' = 2\\\\ou\\\\x''=\frac{-5-\sqrt{81} }{2} \\\\x''=\frac{-5-9 }{2} = \frac{-14}{2} \\\\x'' = -7\:\:\: n\~ao\:\:conve\´m$