MathDB

9

Part of 2010 Hanoi Open Mathematics Competitions

Problems(2)

area computational (2010 HOMC Junior Q9)

Source:

7/18/2019
Let be given a triangle ABCABC and points D,M,ND,M,N belong to BC,AB,ACBC,AB,AC, respectively. Suppose that MDMD is parallel to ACAC and NDND is parallel to ABAB. If S△BMD=9S_{\vartriangle BMD} = 9 cm 2,S△DNC=25^2, S_{\vartriangle DNC} = 25 cm2^2, compute S△AMNS_{\vartriangle AMN}?
geometryarea of a triangleareas
x,y\in N*, 3x^2+x=4y^2+y => x-y perfect integer (HOMC 2010 Q9)

Source:

7/25/2019
Let x,yx,y be the positive integers such that 3x2+x=4y2+y3x^2 +x = 4y^2 + y. Prove that x−yx - y is a perfect (square).
number theorydiophantine