Resolva as equações com fatorial a seguir .
a- 2(x-4)! =(x-2)!
b - n! - 12 (n - 1 )! = 0
c - n!
(n - 2 ) ! = 30
ME AJUDE POR FAVOR PRECISO PRA HOJE
mikestonoga:
ta meio confuso seu enunciado, consegue tirar uma foto?
Desculpa mais n porque o meu cel quebrou a camera
A) 2(x-4)!=(x-2!
B) n!-12(n-1)!=0
C)(n!)/(n-2)!=30
isso?
ss
Soluções para a tarefa
Respondido por
1
A) ![2(x-4)!=(x-2)! \\ 2= \frac{(x-2)!}{(x-4)!} \\ 2= \frac{(x-2)!}{(x-4)(x-3)(x-2)!} \\ 2= \frac{1}{(x-4)(x-3)} \\ 2= \frac{1}{ x^{2} -3x-4x+12} \\ 2( x^{2} -3x-4x+12)=1 \\ 2 x^{2} -6x-8x+24=1 \\ 2x^2-14x+23=0 \\ x'= \frac{14+ \sqrt{196-184}}{2.2} \\ x'= \frac{14+ \sqrt{12}}{4} \\ x''= \frac{14- \sqrt{12}}{4} \\ S= \left[\begin{array}{ccc} \frac{14+ \sqrt{12}}{4}; \frac{14- \sqrt{12}}{4} \end{array}\right] }](https://tex.z-dn.net/?f=2%28x-4%29%21%3D%28x-2%29%21+%5C%5C+2%3D+%5Cfrac%7B%28x-2%29%21%7D%7B%28x-4%29%21%7D++%5C%5C+2%3D+%5Cfrac%7B%28x-2%29%21%7D%7B%28x-4%29%28x-3%29%28x-2%29%21%7D++%5C%5C+2%3D+%5Cfrac%7B1%7D%7B%28x-4%29%28x-3%29%7D+%5C%5C+2%3D+%5Cfrac%7B1%7D%7B+x%5E%7B2%7D+-3x-4x%2B12%7D++%5C%5C+2%28+x%5E%7B2%7D+-3x-4x%2B12%29%3D1+%5C%5C+2+x%5E%7B2%7D+-6x-8x%2B24%3D1+%5C%5C+2x%5E2-14x%2B23%3D0+%5C%5C+x%27%3D+%5Cfrac%7B14%2B+%5Csqrt%7B196-184%7D%7D%7B2.2%7D+%5C%5C+x%27%3D+%5Cfrac%7B14%2B+%5Csqrt%7B12%7D%7D%7B4%7D++%5C%5C+x%27%27%3D+%5Cfrac%7B14-+%5Csqrt%7B12%7D%7D%7B4%7D+%5C%5C+S%3D++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D+%5Cfrac%7B14%2B+%5Csqrt%7B12%7D%7D%7B4%7D%3B+%5Cfrac%7B14-+%5Csqrt%7B12%7D%7D%7B4%7D++%5Cend%7Barray%7D%5Cright%5D+%7D+ "2(x-4)!=(x-2)! \\ 2= \frac{(x-2)!}{(x-4)!} \\ 2= \frac{(x-2)!}{(x-4)(x-3)(x-2)!} \\ 2= \frac{1}{(x-4)(x-3)} \\ 2= \frac{1}{ x^{2} -3x-4x+12} \\ 2( x^{2} -3x-4x+12)=1 \\ 2 x^{2} -6x-8x+24=1 \\ 2x^2-14x+23=0 \\ x'= \frac{14+ \sqrt{196-184}}{2.2} \\ x'= \frac{14+ \sqrt{12}}{4} \\ x''= \frac{14- \sqrt{12}}{4} \\ S= \left[\begin{array}{ccc} \frac{14+ \sqrt{12}}{4}; \frac{14- \sqrt{12}}{4} \end{array}\right] }")
B)
C)![\frac{n!}{(n-2)!}=30 \\ \frac{n.(n-1)(n-2)!}{(n-2)!}=30 \\ n.(n-1)=30 \\ n^2-n=30 \\ n^2-n-30=0 \\ \\ n'= \frac{1+ \sqrt{121}}{2} \\ n'= \frac{1+11}{2} \\ n'= \frac{12}{2} \\ n'=6 \\ \\ n''= \frac{1- \sqrt{121}}{2} \\ n''= \frac{1-11}{2} \\ n''= \frac{10}{2} \\ n''=5 \\ \\ S= \left[\begin{array}{ccc}5;6\end{array}\right]](https://tex.z-dn.net/?f=+%5Cfrac%7Bn%21%7D%7B%28n-2%29%21%7D%3D30+%5C%5C+%5Cfrac%7Bn.%28n-1%29%28n-2%29%21%7D%7B%28n-2%29%21%7D%3D30++%5C%5C+n.%28n-1%29%3D30+%5C%5C+n%5E2-n%3D30+%5C%5C+n%5E2-n-30%3D0+%5C%5C++%5C%5C+n%27%3D+%5Cfrac%7B1%2B+%5Csqrt%7B121%7D%7D%7B2%7D++%5C%5C+n%27%3D+%5Cfrac%7B1%2B11%7D%7B2%7D++%5C%5C+n%27%3D+%5Cfrac%7B12%7D%7B2%7D++%5C%5C+n%27%3D6+%5C%5C++%5C%5C+n%27%27%3D+%5Cfrac%7B1-+%5Csqrt%7B121%7D%7D%7B2%7D++%5C%5C+n%27%27%3D+%5Cfrac%7B1-11%7D%7B2%7D++%5C%5C+n%27%27%3D+%5Cfrac%7B10%7D%7B2%7D++%5C%5C+n%27%27%3D5+%5C%5C++%5C%5C+S%3D++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%3B6%5Cend%7Barray%7D%5Cright%5D+ "\frac{n!}{(n-2)!}=30 \\ \frac{n.(n-1)(n-2)!}{(n-2)!}=30 \\ n.(n-1)=30 \\ n^2-n=30 \\ n^2-n-30=0 \\ \\ n'= \frac{1+ \sqrt{121}}{2} \\ n'= \frac{1+11}{2} \\ n'= \frac{12}{2} \\ n'=6 \\ \\ n''= \frac{1- \sqrt{121}}{2} \\ n''= \frac{1-11}{2} \\ n''= \frac{10}{2} \\ n''=5 \\ \\ S= \left[\begin{array}{ccc}5;6\end{array}\right]")
B)
C)
se puder considerar melhor resposta, se vc entender é claro
entendeu?
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