Question

pe multimea numerelor reale se defineste legea de compozitie asociativa x * y = x+y-1 . determinati numarul natural n,n >= 2 , pentru care combinari de n luate de cate 1 * combinari de n luate de cate 2 = 14

Answer 1

[tex] C_{n} ^{1} * C_{n} ^{2} =14 \\ \frac{n!}{1!(n-1)!} + \frac{n!}{2!(n-2)!} =15 \\ \frac{(n-1)!n}{1!(n-1)!} + \frac{n-2)!(n-1)n}{2!(n-2)!} =15 \\ n+ \frac{n(n-1)}{2} =15 \\ 2n+ n^{2} -n-30=0 \\ n^{2} +n-30=0 \\ delta=1+120=121= 11^{2} \\ n_{1} = \frac{-1+11}{2} =5 \\ n_{2} = \frac{-1-11}{2} =-6 \\ S={5}[/tex]