Question

(k-10)!=77(k-11)!
решите уравнение

Answer 1

$(k - 10)! = 77(k - 11)!\\ n! = 1cdot 2 cdot 3 cdot ... cdot (n - 1) cdot n, 0! = 1; n! ne 0, n in mathbb{N}; k geq 11 \\ (k - 10)! = 77(k - 11)! | : (k - 11)!\\ frac{(k - 10)!}{(k - 11)!} = 77\\ frac{1 cdot 2 cdot (k - 11) cdot (k - 10)}{1 cdot 2 cdot (k - 11)} = 77\\ k - 10 = 77, boxed{k = 87}$