... BD.A DCBBy the Thales theorem we getOEBC+OFAD=ODBD+OCAC=ODBD+OBBD= 1. From this,1OE=1BC+1AD. Likewise,1OF=1BC+1AD. Hence, OE = OF . That is,2EF=1OE=1BC+1AD=13+16=12. ... y) = |x − y| + |x3− y3|when x, y vary satisfying the restriction x2+ y2= 1.Rewriting this asf(x, y) = |x − y|(1 + x2+ xy + y2) = |x − y|(2 + xy).from which we square to arrive ... xy33=533.Hence,f(x, y) ≤53.53.Equality occurs whenxy = −13, x2+ y2= 1.This simultaneous equations are equivalent toxy = −13, x + y =1√3.5Hanoi Open Mathematical...