Решите уравнения: 1)(k+1)!/k!=12; 2)(m+1)!/(m-1)!=30 ; 3)A^2 x+1=420; 4)2C^3 x=4/7 C^4 x+2

1) [latex] \frac{(k+1)!}{k!} = \frac{k!(k+1)}{k!}=k+1 [/latex] k+1=12, k=11 2) [latex] \frac{(m+1)!}{(m-1)!} = \frac{(m-1)!m(m+1)}{(m-1)!}= \frac{m(m+1)}{1}=m^2+m [/latex] m²+m=30, m²+m-30=0, D=1+120=121, √121=11 m1=(-1-11)/2=-6 m2=(-1+11)/2=5 3)[latex] A^2_{x+1}= \frac{(x+1)!}{(x+1-2)!}= \frac{(x+1)!}{(x-1)!} =x(x+1)=420 [/latex] x²+x-420=0 D=1+1680=1681, √1681=41 x1=(-1-41)/2=-21 x2=(-1+41)/2=20 ответ: х1=-21.  х2=20 4) [latex] \frac{2x!}{3!(x-3)!}= \frac{4(x+2)!}{7*4!(x+2-4)!} [/latex] [latex] \frac{2(x-3)!(x-2)(x-1)x}{3!(x-3)!}= \frac{4(x-2)!(x-1)x(x+1)(x+2)}{7*4!(x-2)!}  [/latex] 14(x-2)=(x+1)(x+2) 14x-28=(x²+3x+2) x²+3x+2-14x+28=0 x²-11x+30=0,  D=121-120=1, х1=(11+1)/2=6,  х2=(11-1)/2=5