MathDB

1

Part of 2014 Bosnia And Herzegovina - Regional Olympiad

Problems(4)

Regional Olympiad - FBH 2014 Grade 9 Problem 1

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2014

9/24/2018
Find all possible values of (a+b−c)2(a−c)(b−c)+(b+c−a)2(b−a)(c−a)+(c+a−b)2(c−b)(a−b)\frac{(a+b-c)^2}{(a-c)(b-c)}+\frac{(b+c-a)^2}{(b-a)(c-a)}+\frac{(c+a-b)^2}{(c-b)(a-b)}
valuealgebra
Regional Olympiad - FBH 2014 Grade 10 Problem 1

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2014

9/24/2018
Solve the equation: xyz+yzx+zxy=3 \frac{xy}{z}+\frac{yz}{x}+\frac{zx}{y}=3 where xx, yy and zz are integers
equaionnumber theory
Regional Olympiad - FBH 2014 Grade 11 Problem 1

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2014

9/24/2018
Solve logarithmical equation xlog⁡3x−1+2(x−1)log⁡3x=3x2x^{\log _{3} {x-1}} + 2(x-1)^{\log _{3} {x}}=3x^2
logarithmsalgebraequation
Regional Olympiad - FBH 2014 Grade 12 Problem 1

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2014

9/24/2018
Find all real solutions of the equation: x=2z21+z2x=\frac{2z^2}{1+z^2} y=2x21+x2y=\frac{2x^2}{1+x^2} z=2y21+y2z=\frac{2y^2}{1+y^2}
real numbersalgebraequation