MathDB

3

Part of 1994 Cono Sur Olympiad

Problems(2)

Find minimun value

Source: Cono Sur 1994-problem 3

6/1/2006
Let pp be a positive real number given. Find the minimun vale of x3+y3x^3+y^3, knowing that xx and yy are positive real numbers such that xy(x+y)=pxy(x+y)=p.
inequalitiesinequalities unsolved
Prove area

Source: Cono Sur 1994-problem 6

6/1/2006
Consider a △ABC\triangle {ABC}, with AC⊥BCAC \perp BC. Consider a point DD on ABAB such that CD=kCD=k, and the radius of the inscribe circles on △ADC\triangle {ADC} and △CDB\triangle {CDB} are equals. Prove that the area of △ABC\triangle {ABC} is equal to k2k^2.
geometry