MathDB

2

Part of 2014 Bosnia And Herzegovina - Regional Olympiad

Problems(3)

Regional Olympiad - FBH 2014 Grade 9 Problem 2

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2014

9/24/2018
Solve the equation, where xx and yy are positive integers: x3−y3=999 x^3-y^3=999
algebraequation
Regional Olympiad - FBH 2014 Grade 10 Problem 2

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2014

9/24/2018
Let aa, bb and cc be positive real numbers such that ab+bc+ca=1ab+bc+ca=1. Prove the inequality: 1a+1b+1c≥3(a+b+c)\frac{1}{a}+\frac{1}{b}+\frac{1}{c} \geq 3(a+b+c)
algebrainequalities proposedInequality
Regional Olympiad - FBH 2014 Grade 11 Problem 2

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2014

9/24/2018
Solve the equation x2+y2+z2=686x^2+y^2+z^2=686 where xx, yy and zz are positive integers
number theorypositive integerequation