Question

14. Sa se rezolve:
(probleme de numărare clasa a X-a)​

Answer 1

Răspuns:

..x=4;y=8

Explicație pas cu pas:

impartim prima relati cu(x-1)!(y-1)!

y=2x

in locuim in a doua

obtinem

5x²=80

x²=16 cum x e natural...x=4⇒y=8

Answer 2

$\it (x-1)!y!=2(y-1)!x! \Rightarrow (x-1)!(y-1)!\cdot y=2(y-1)!(x-1)!\cdot x\Big|_{:(x-1)!(y-1)!} \Rightarrow \\ \\ \\ \Rightarrow y=2x\ \ \ \ \ (*)\\ \\ \\ x^2+y^2=80 \stackrel{(*)}{\Longrightarrow} x^2+(2x)^2}=80 \Rightarrow x^2+4x^2=80 \Rightarrow\\ \\ \Rightarrow 5x^2=80\Big|_{:5} \Rightarrow x^2=16 \Rightarrow x=4\\ \\ \\ x=4\ \stackrel{(*)}{\Longrightarrow}\ y=2\cdot4 \Rightarrow y=8$