Problem C. 1095. (November 2011)
C. 1095. Which product is greater: or ?
(5 pont)
Deadline expired on December 12, 2011.
Sorry, the solution is available only in Hungarian. Google translation
Megoldás. Legyen \(\displaystyle a=111\ 111\ 111\ 111\). Ekkor az összehasonlítandó szorzatok \(\displaystyle B=(5a-2)(6a+3)\) és \(\displaystyle J=(5a+2)(6a-2)\), azaz \(\displaystyle B=30a^2 +3a -6\) és \(\displaystyle J=30a^2 -4\). Mivel \(\displaystyle B-J=3a-2>0\), ezért a bal oldali szorzat nagyobb, mint a jobb oldali.
Statistics:
463 students sent a solution. 5 points: 338 students. 4 points: 40 students. 3 points: 29 students. 2 points: 15 students. 1 point: 8 students. 0 point: 21 students. Unfair, not evaluated: 12 solutionss.
Problems in Mathematics of KöMaL, November 2011