Question

Calcule o valor de x na equação 6 Cx,2 = Ax,3

Answer 1

$C_{m,p}=\frac{m!}{(m-p)! \ p!}\\ \\C_{x,2}=\frac{x!}{(x-2)! \ 2!}=\frac{x\cdot(x-1)\cdot(x-2)!}{(x-2)! \ 2\cdot1}=\frac{x\cdot(x-1)}{2}\\ \\A_{m,p}=\frac{m!}{(m-p)!}\\ \\\\A_{x,3}=\frac{x!}{(x-3)!}=\frac{x\cdot(x-1)\cdot(x-2)\cdot(x-3)!}{(x-3)!}=x^3-3x^2+2x$

$6\cdot C_{x,2}=A_{x,3}\\ \\6\cdot\left[\frac{x\cdot(x-1)}{2}\right]=x\cdot(x-1)\cdot(x-2)\\ \\2\cdot3\cdot\left[\frac{x\cdot(x-1)}{2}\right]=x\cdot(x-1)\cdot(x-2)\\ \\3=x-2\\ \\x-2=3\\ \\x=3+2\\ \\x=5$

Veja prova real
$6\cdot C_{5,2}=A_{5,3}\\ 6\cdot 10=60\\ 60=60$