MathDB

1

Part of 2015 Bosnia And Herzegovina - Regional Olympiad

Problems(4)

Regional Olympiad - FBH 2015 Grade 9 Problem 1

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2015

9/23/2018
Find all positive integers aa and bb such that ab+1∣a2−1 ab+1 \mid a^2-1
number theoryDivisibility
Regional Olympiad - FBH 2015 Grade 10 Problem 1

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2015

9/23/2018
Solve the inequation: 5∣x∣≤x(3x+2−28−2x−x2)5\mid x\mid \leq x(3x+2-2\sqrt{8-2x-x^2})
algebrainequation
Regional Olympiad - FBH 2015 Grade 11 Problem 1

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2015

9/23/2018
For real numbers xx, yy and zz, solve the system of equations: x3+y3=3y+3z+4x^3+y^3=3y+3z+4 y3+z3=3z+3x+4y^3+z^3=3z+3x+4 x3+z3=3x+3y+4x^3+z^3=3x+3y+4
algebrasystem of equations
Regional Olympiad - FBH 2015 Grade 12 Problem 1

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2015

9/23/2018
Let aa, bb, cc and dd be real numbers such that a+b+c+d=8a+b+c+d=8. Prove the inequality: a8+b−d3+b8+c−a3+c8+d−b3+d8+a−c3≥4\frac{a}{\sqrt[3]{8+b-d}}+\frac{b}{\sqrt[3]{8+c-a}}+\frac{c}{\sqrt[3]{8+d-b}}+\frac{d}{\sqrt[3]{8+a-c}} \geq 4
inequalitiesalgebra