1

Part of 2005 Vietnam National Olympiad

Problems(2)

Find the greatest value and the smallest value of x+y

Source: VietnamMO2005,problem1

x,y

be real numbers satisfying the condition:

x-3\sqrt {x+1}=3\sqrt{y+2} -y

Find the greatest value and the smallest value of:

P=x+y

inequalities proposedinequalitiesalgebraVietnam

f(f(x - y)) = f(x)f(y) - f(x) + f(y) - xy

Source: VietNamMO 2005,problem4

Find all function

f: \mathbb R\to \mathbb R

satisfying the condition: f(f(x \minus{} y)) \equal{} f(x)\cdot f(y) \minus{} f(x) \plus{} f(y) \minus{} xy

functionalgebra proposedalgebra