MathDB

4

Part of 2006 Junior Balkan Team Selection Tests - Moldova

Problems(2)

Poblem 4 (1st jbmo tst), moldova

Source: 1st JBMO TST, Moldova

3/31/2006
Let nn be a positive integer, n≥4n\geq 4. nn cards are arranged on a circle and the numbers 11 or −1-1 are written on each of the cards. in a questionquestion we may find out the product of the numbers on any 33 cards. What is the minimum numbers if questions needed to find out the product of all nn numbers?
combinatorics proposedcombinatorics
Poblem 4 (2nd jbmo tst)

Source: 2nd TST for JBMO, Moldova

3/31/2006
Determine all real solutions of the equation: x2x−1+x−1+x−1x2=x−1x2+1x−1+x2x−1.{ \frac{x^{2}}{x-1}+\sqrt{x-1}+\frac{\sqrt{x-1}}{x^{2}}}=\frac{x-1}{x^{2}}+\frac{1}{\sqrt{x-1}}+\frac{x^{2}}{\sqrt{x-1}} .
quadraticsalgebraalgebra proposed