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Ae mano,
basta aplicar o mesmo conceito de fatorial para combinação simples, lembrando que x ∈ IN (o elemento do conjunto solução deve pertencer ao conjunto dos números naturais), vamos lá:
![\dfrac{(x+3)!}{2![(x+3)-2]!}=15\\\\\\
\dfrac{(x+3)\cdot(x+2)\cdot(x+1)!}{2!(x+1)!}=15\\\\\\
\dfrac{(x+3)\cdot(x+2)}{2}=15\\\\
x^2+2x+3x+6=15\cdot2\\
x^2+5x+6=30\\\\
x^2+5x-24=0~~(eq.~do~2^o~grau)\\\\
x_1=3~~e~~x_2=-8~~(\notin~\mathbb{N})\\\\\\
\Large\boxed{\text{S}=\{3\}}](https://tex.z-dn.net/?f=+%5Cdfrac%7B%28x%2B3%29%21%7D%7B2%21%5B%28x%2B3%29-2%5D%21%7D%3D15%5C%5C%5C%5C%5C%5C%0A+%5Cdfrac%7B%28x%2B3%29%5Ccdot%28x%2B2%29%5Ccdot%28x%2B1%29%21%7D%7B2%21%28x%2B1%29%21%7D%3D15%5C%5C%5C%5C%5C%5C%0A+%5Cdfrac%7B%28x%2B3%29%5Ccdot%28x%2B2%29%7D%7B2%7D%3D15%5C%5C%5C%5C%0Ax%5E2%2B2x%2B3x%2B6%3D15%5Ccdot2%5C%5C%0Ax%5E2%2B5x%2B6%3D30%5C%5C%5C%5C%0Ax%5E2%2B5x-24%3D0%7E%7E%28eq.%7Edo%7E2%5Eo%7Egrau%29%5C%5C%5C%5C%0Ax_1%3D3%7E%7Ee%7E%7Ex_2%3D-8%7E%7E%28%5Cnotin%7E%5Cmathbb%7BN%7D%29%5C%5C%5C%5C%5C%5C%0A%5CLarge%5Cboxed%7B%5Ctext%7BS%7D%3D%5C%7B3%5C%7D%7D+++ "\dfrac{(x+3)!}{2![(x+3)-2]!}=15\\\\\\
\dfrac{(x+3)\cdot(x+2)\cdot(x+1)!}{2!(x+1)!}=15\\\\\\
\dfrac{(x+3)\cdot(x+2)}{2}=15\\\\
x^2+2x+3x+6=15\cdot2\\
x^2+5x+6=30\\\\
x^2+5x-24=0~~(eq.~do~2^o~grau)\\\\
x_1=3~~e~~x_2=-8~~(\notin~\mathbb{N})\\\\\\
\Large\boxed{\text{S}=\{3\}}")
Tenha ótimos estudos :)
basta aplicar o mesmo conceito de fatorial para combinação simples, lembrando que x ∈ IN (o elemento do conjunto solução deve pertencer ao conjunto dos números naturais), vamos lá:
Tenha ótimos estudos :)
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