Question

o multime are 42 submultimi ordonate cu 2 elemente. sa sa afle nr elementelor multimii.

Answer 1

[tex]\text{Daca sunt submultimi ordonate,e clar ca ne gandim la aranjamente:}\\ \text{Notam cu x numarul de elemente si obtinem:}\\ A_x^2=42\\ \dfrac{x!}{(x-2)!}=42\\ \dfrac{(x-2)!(x-1)\cdot x}{(x-2)!}=42\\ (x-1)x=42\\ x^2-x-42=0\\ \Delta=1+4\cdot 42=169\Rightarrow \sqrt{\Delta}=13\\ x_1=\dfrac{1+13}{2}=\dfrac{14}{2}=7\\ x_2=\dfrac{1-13}{2}=-6(\text{solutia aceasta nu convine})\\ \text{Prin urmare:}\\ S=7[/tex]