MathDB

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Part of 2012 Middle European Mathematical Olympiad

Problems(2)

Functional equation on positive reals

Source: Middle European Mathematical Olympiad 2012 - Individuals I-1

9/14/2012
Let R+ \mathbb{R} ^{+} denote the set of all positive real numbers. Find all functions R+→R+ \mathbb{R} ^{+} \to \mathbb{R} ^{+} such that f(x+f(y))=yf(xy+1) f(x+f(y)) = yf(xy+1) holds for all x,y∈R+ x, y \in \mathbb{R} ^{+} .
functionalgebrafunctional equationalgebra proposedInequality
3 variable equation

Source: Middle European Mathematical Olympiad 2012 - Team Compt. T-1

9/14/2012
Find all triplets (x,y,z) (x,y,z) of real numbers such that 2x3+1=3zx 2x^3 + 1 = 3zx 2y3+1=3xy 2y^3 + 1 = 3xy 2z3+1=3yz 2z^3 + 1 = 3yz
algebrasystem of equationsalgebra proposed