Question

Determine $x$ na equação $A_{x,3} - 6$ . $C_{x,2} = 0$

Answer 1

$A_{x,3}~-~6~.~C_{x,2}~=~0\\\\\\\frac{x!}{(x-3)!}~-~6~.~\frac{x!}{2!.(x-2)!}~=~0\\\\\\\frac{x~.~(x-1)~.~(x-2)~.~(x-3)!}{(x-3)!}~=~6~.~\frac{x~.~(x-1)~.~(x-2)!}{2.(x-2)!}\\\\\\\frac{x~.~(x-1)~.~(x-2)~.~1}{1}~=~3~.~\frac{x~.~(x-1)~.~1}{1}\\\\\\\frac{x~.~(x-1)~.~(x-2)}{x~.~(x-1)}~=~3\\\\\\x-2~=~3\\\\\\x~=~3+2\\\\\\\boxed{x~=~5}$