<prompt> Acha x, y, na z ziwe nambari halisi zisizo hasi kama kwamba x y z 2. Pata thamani ya juu zaidi yax2 - xy y2x2 - xz z2y2 - yz z2.  <response>: Bila hasara ya jumla, tunaweza kudhani kuwa z le x na z le y. Kishax2 - xy y2x2 - xz z2y2 - yz z2 le x2 - xy y2 x 2 y2.Na AM-GM,anzaalignx2 y2 x2 - xy y2 frac49 kushoto frac32 xy kulia kushoto frac3 2 xy kulia x2 - xy y2 le frac49 kushoto fracfrac32 xy frac32 xy x2 - xy y2 3 kulia3 frac49 kushoto fracx2 2xy y23 kulia3 frac49 cdot fracx y627 le frac4243 x y z6 frac256243.endalignUsawa hutokea wakati x frac43, y frac23, na z 0, hivyo thamani ya juu zaidi ni frac 256243. 