Question

Va rog ajutati-ma , ma chinui la acest exercitiu de cateva ore.
Determinati x astfel incat C de x luate cate 2 + A de x luate cate 2 = 30 . X apartine lui N. VA ROOOG

Answer 1

Se impune ca x ≥ 2

Ecuatia devine

$\frac{x!}{2!(x-2)!}+ \frac{x!}{(x-2)!} =30 \\ \frac{x(x-1)}{2}+x(x-1)=30\ \ \ /\cdot2 \\ x(x-1)+2x(x-1)=60 \\ x^2-x+2x^2-2x=60 \\ 3x^2-3x-60=0$
Impartim prin 3

$x^2-x-20=0 \\ \Delta=1+80=81 \\ x_1= \frac{1+9}{2}=5 \\ x_2= \frac{1-9}{2}=-4\ nu\ convine \\ Raspuns:\ x=5$