Verified answer

Ответ:

Формулы:  

[tex]A_{n}^{m}=n(m-1)\cdot ...\cdot (n-m+1)\ \ ,\ \ P_{n}=n!\ \ ,\ \ (n+1)!=n!\, (n+1)[/tex]

[tex]\dfrac{A_{x}^4\cdot P_{x-4}}{P_{x-2}}=42[/tex]  

[tex]\dfrac{x\, (x-1)(x-2)(x-3)\cdot (x-4)!}{(x-2)!}=42\ \ ,\\\\\\\dfrac{x\, (x-1)(x-2)(x-3)\cdot (x-4)!}{(x-4)!\cdot (x-3)(x-2)}=42\ \ ,\ \ \ x\, (x-1)=42\ \ ,\\\\\\x^2-x-42=0\ \ ,\ \ \ x_1=-6\ ,\ x_2=7\ \ (teorema\ Vieta)\\\\x_1=-6 < 0\ \ \ ne\ podxodit\\\\Otvet:\ x=7\ .[/tex]