[tex]b)x \geq 0 \\ \frac{(x+2)!}{(x+2-2)!}=56(x+2) \\ (x+1)(x+2)=56(x+2) \\ (x+2)(x+1-56)=0 \\ x+2=0saux-55=0 \\ x=-2sau x=55 \\ deci,x=55 \\ c) \frac{(x+1)!}{(x-1)!}=30 \\ x(x+1)=30 [/tex]
[tex] x^{2} +x-30=0 \\ x=-6;x=5 \\ solutia -este :x=5 \\ d) \frac{(n-1)!}{(n-6)!}=18* \frac{(n-3)!}{(n-7)!} \\ n \geq 7 \\ \frac{(n-1)!-18(n-3)!(n-6)}{(n-6)!} =0 \\ (n-3)![(n-2)(n-1)-18n+108)]=0 \\ n^2-3n+2-18n+108=0 \\ n^2-21n+110=0 \\ n=10;n=11 \\ e) \frac{x!}{(x-2)!} +2 \frac{(x+1)!}{(x-1)!} =30 \\ x \geq 2;xdinN \\ (x-1)x+2x(x+1)-30=0 \\ 3 x^{2} +x-30=0 \\ x=-2;x=5/3 \\ ec.nu.are.solutii \\ f) \frac{(x+1)!}{2}=360 \\ (x+1)!=720 \\ x+1=6 \\ x=5 \\ g)(x+3)!=10(x+2)! \\ (x+2)![(x+3)-10]=0 \\ x-7=0 \\ x=7 [/tex]
