Răspuns:
6
Explicație pas cu pas:
[tex]C_{x+1}^{2}+A_{x}^{2}=51,~~\dfrac{(x+1)!}{2!*(x+1-2)!} +\dfrac{x!}{(x-2)!} =51,~\dfrac{(x-1)!*x*(x+1)}{2*(x-1)!}+\dfrac{(x-2)!*(x-1)*x}{(x-2)!}=51,~~\dfrac{x(x+1)}{2} +\dfrac{(x-1)x}{1} =51~|*2,~~[/tex]
Obținem, x(x+1)+2x(x-1)=102, ⇒x(x+1+2x-2)=102, ⇒x(3x-1)=102,⇒3x²-x-102=0, Δ=(-1)²-4·3·(-102)=1225=35², deci x=(1+35)/(2·3)=6.
Valoarea negativă pentru x nu convine, deoarece x∈N
