3

Part of 2010 JBMO Shortlist

Problems(2)

JBMO 2010 Shortlist A3

Source: JBMO 2010 Shortlist

(x,y)

of real numbers such that

|x|+ |y|=1340

x^{3}+y^{3}+2010xy= 670^{3}

algebraequationJBMO Shortlist

2010 JBMO Shortlist G2

Source: 2010 JBMO Shortlist G2

Consider a triangle

{ABC}

{M}

be the midpoint of the side

{BC.}

{\angle MAC=\angle ABC}

{\angle BAM=105^{\circ}.}

Find the measure of

{\angle ABC}