Question

Doar ecuatia de la d)

Answer 1

Răspuns:

Explicație pas cu pas:

$\frac{(x-1)!}{(x-3)!2!}+\frac{(x-3)!}{(x-5)!}=101\\\frac{(x-2)(x-1)}{2}+(x-4)(x-3)=101 \rightarrow x^2-3x+2+2(x^2-7x+12)=202\rightarrow\\\rightarrow 3x^2-17x+26=202 \rightarrow 3x^2-17x-176=0\\\Delta=289+2112=2401 \rightarrow \sqrt{\Delta}=49\\x_1=\frac{17+49}{6}=11\\x_{2}<0 \quad \text{nu are sens sa discuti despre factorial negativ ca nu ai invatat functia gamma}\\\text{cum} \quad x>3 \rightarrow x=11 \quad \text{solu\c{t}ie}$