Răspuns :
Răspuns:
Explicație pas cu pas:
[tex]C_n^1+C_n^2=15, ~~=>n~natural,~n\geq 2.\\\dfrac{n!}{1!*(n-1)!}+\dfrac{n!}{2!*(n-2)!}=15,~=>~\dfrac{(n-1)!*n}{1!*(n-1)!}+\dfrac{(n-2)!*(n-1)*n}{2!*(n-2)!}=15,~=>~n+\dfrac{(n-1)*n}{2}=15~|*2,~=>~2n+(n-1)*n=2*15[/tex]
⇒2n+n²-n-30=0, ⇒n²+n-30=0, Δ=1²-4·1·(-30)=1+120=121=11², deci
n=(-1-11)/2=-6, nu convine
n=(-1+11)/2=5.
Răspuns: n=5.
Răspuns:
Explicație pas cu pas:
n!/1!(n - 1)! + n!/2!(n - 2)! = 15
n(n - 1)! / (n - 1)! + n(n - 1)(n - 2)!/2(n - 2)! = 15
n + n(n - 1)/2 = 15
2n + n(n - 1) = 30
2n + n^2 - n - 30 = 0
n^2 + n - 30 = 0
Δ = 1 + 120 = 121
n = numar intreg pozitiv
n = (-1 + 11)/2 = 10/2 = 5