Question

решите уравнение по теме: Бином Ньютона
5*C^3_n=C^4_n+2

Answer 1

$displaystyle 5C_n^3=C_{n+2}^4\\5* frac{n!}{3!(n-3)!}= frac{(n+2)!}{4!(n+2-4)!}\\5 frac{n!}{3!(n-3)!}= frac{n!(n+1)(n+2)}{3!*4*(n-3)!(n-2)}\\ 5frac{1}{1}= frac{(n+1)(n+2)}{4(n-2)}\\20(n-2)=(n+1)(n+2)\\20n-40=n^2+3n+2\\n^2-17n+42=0\\D=289-168=121=11^2\\n_1=3; n_2=14$