Kombinatorika

2010007103

Časť: 
B
Pre všetky \(x\in \mathbb{N}\), \(x \geq 2\) určte množinu všetkých riešení danej nerovnice. \[ \left({ x\above 0.0pt x - 2}\right)\cdot \left({x\above 0.0pt 2}\right) - 20\cdot \left({x\above 0.0pt 2}\right) + 96 < 0 \]
\(\{5\}\)
\(\{9;10;11\}\)
riešenie neexistuje
\( (8;12)\)

9000136901

Časť: 
B
Zjednodušte \(\left({15\above 0.0pt 8} \right) +\left ({15\above 0.0pt 9} \right)\).
\(\left({16\above 0.0pt 9} \right)\)
\(\left({15\above 0.0pt 10}\right)\)
\(\left({15\above 0.0pt 7} \right)\)
\(\left({16\above 0.0pt 8} \right)\)
\(\left({30\above 0.0pt 17}\right)\)

9000136903

Časť: 
B
Zjednodušte \(\left({4\above 0.0pt 0}\right) +\left ({4\above 0.0pt 1}\right) +\left ({4\above 0.0pt 2}\right) +\left ({4\above 0.0pt 3}\right) +\left ({4\above 0.0pt 4}\right)\).
\(4^{2}\)
\(14\)
\(\left({5\above 0.0pt 4}\right)\)
\(32\)
\(\left({8\above 0.0pt 4}\right)\)