Question

ex. 1,2,6,7,8 . multumesc anticipat 

Answer 1

1) Nu se vede bine enuntul. Daca este asa:
$2^{x!}\leq2048\Rightarrow x!\leq11\Rightarrow x\in\{0;1;2;3\}$
2)
$A_n^3=n(n-1)(n-2)\ \vdots3$ deoarece produsul a trei numere consecutive se divide la 3 (in general, produsul a n numere consecutive se divide la n)
6)
$\dfrac{(2x-3)(2x-4)}{1\cdot2}=3\Rightarrow(2x-3)(2x-4)=6$ (produsul a doua numere naturale consecutive este 6) deci 2x-4=2⇒x=3
7)
$\dfrac{x(x-1)}{2}+x(x-1)=30\Rightarrow 3x(x-1)=60\Rightarrow x(x-1)=30\Rightarrow$
$\Rightarrow x-1=5\Rightarrow x=6$
8)
$n+\dfrac{n(n-1)}{2}=120\Rightarrow n^2+n=240\Rightarrow n(n+1)=15\cdot16\Rightarrown=15$