Question

determinati n apartine N, n>=2 pt care Cn^2+An^2=18(Cn sunt combinari si An sunt aranjamente)

Answer 1

$C_{n} ^{2} + A_{n} ^{2} =18$

n!/[2!•(n-2)!]+n!/(n-2)!=18

n(n-1)(n-2)!/[2!•(n-2)!]+n(n-1)(n-2)!/(n-2)!=18; inmultim cu 2

n(n-1)+2n(n-1)=36

n²-n+2n²-2n=36

3n²-3n=36;   /:3

n²-n=12

n(n-1)=4•3; n≥2

=>n=4