Question

aranjamente de x+2 luate cate 2 - combinari de x+2 luate cate 2 = 28

Answer 1

 

$\displaystyle\bf\\A_{x+2}^2-C_{x+2}^2=28,~~x\in N\\\\A_{x+2}^2-\frac{A_{x+2}^2}{P_2}=28\\\\(x+2)(x+1)-\frac{(x+2)(x+1)}{2}=28\\\\ \frac{2(x+2)(x+1)}{2}-\frac{(x+2)(x+1)}{2}=28~~~\Big|~\cdot2\\\\2(x+2)(x+1)-(x+2)(x+1)=56\\\\(x+2)(x+1)=56\\\\(x+2)(x+1)~~~\text{Este un produs de numere consecutive cu}~~x+2>x+1\\\\\text{Descompunem pe 56 in produs de numere consecutive.}\\\\(x+2)(x+1)=8\cdot7\\\\\implies x+2=8\\\\x=8-2\\\\\boxed{\bf~x=6}$