Question

Solução da equação x!/2!(x-2)! + 3(x-1)!/2(x-3)!=91

Answer 1

$\frac{x!}{2!(x-2)!}+\frac{3(x-1)!}{2(x-3)!}=91\\\\ \frac{x(x-1)(x-2)!}{2!(x-2)!}+\frac{3(x-1)(x-2)(x-3)!}{2(x-3)!}=91\\\\ \frac{x(x-1)}{2}+\frac{3(x-1)(x-2)}{2}=91\ \Rightarrow\ \frac{x(x-1)+3(x-1)(x-2)}{2}=91\\\\ x(x-1)+3(x-1)(x-2)=2.91\\\\ x^2-x+3(x^2-3x+2)=182\\\\ x^2-x+3x^2-9x+6=182\ \Rightarrow\ 4x^2-10x+6=182\\\\ 4x^2-10x+6-182=0\ \Rightarrow\ 4x^2-10x-176=0\\\\ 2x^2-5x-88=0\ \Rightarrow\ a=2\ \| \ b=-5\ \| \ c=-88$

$\Delta=b^2-4ac\ \Rightarrow\ \Delta=(-5)^2-4.2.(-88)\\\\ \Delta=25+704\ \Rightarrow\ \Delta=729\\\\ x_1=\frac{-b+\sqrt{\Delta}}{2a}\ \Rightarrow\ x_1=\frac{-(-5)+\sqrt{729}}{2.2}\\\\ x_1=\frac{5+27}{4}\ \Rightarrow\ x_1=\frac{32}{4}\ \Rightarrow\ x_1=8\mid \exists\ x!\\\\ x_2=\frac{-b-\sqrt{\Delta}}{2a}\ \Rightarrow\ x_2=\frac{-(-5)-\sqrt{729}}{2.2}\\\\ x_2=\frac{5-27}{4}\ \Rightarrow\ x_2=\frac{-22}{4}\ \Rightarrow\ x_2=\frac{-11}{2}\mid \nexists\ x!\\\\ Resposta:\ \| \ x=8\ \|$

Answer 2

Resposta:

entao ta errada n da pra intender

Explicação passo-a-passo: