Question

Combinari de x elemente luate cate 3 + combinari de x elemente luate cate 2 = 15(x-1)

Answer 1

[tex]C_x^3+C_x^2=15(x-1)\\ \frac{x!}{(x-3)!3!}+\frac{x!}{(x-2)!2!}=15(x-1)\\ \frac{(x-2)(x-1)x}{6}+\frac{(x-1)x}{3}=15(x-1)|\cdot 6\\ (x-2)(x-1)x+2(x-1)x=90(x-1)\\ (x-2)(x-1)x-88(x-1)=0\\ (x-1)(x^2-2x-88)=0\\ x=1 sau\quad x^2-2x-88=0\\ Deci x=1 [/tex] pt ca rad ec de grad 2 nu sunt naturale pt ca delta=356, deci nu e patrat perfect, deci solutiile vor contine radicali, iar in cazul combinarilor nu putem folosi decat nr naturale.