<prompt> Acha a na b ziwe nambari halisi ili a 2b 0. Pata thamani ya chini zaidi ya3a3 sqrt3 frac2ab - 2b2.  <response>: Kwanza, tunashughulikia neno frac2ab - 2b2 frac2ba - 2b frac42ba - 2b.Thamani ya 2ba - 2b, katika b, inakuzwa wakati 2b fraca2, au b fraca4. Kwa hivyo,frac42ba - 2b ge frac4fraca2 cdot fraca2 frac16a 2.Kisha3a3 sqrt3 frac2ab - 2b2 ge 3a3 sqrt3 frac16a2.Na AM- GM,anzaalign3a3 sqrt3 frac16a2 frac3a3 sqrt32 frac3a3 sqrt3 2 frac163a2 frac163a2 frac163a2 ge 5 sqrt5frac3a3 sqrt32 cdot frac3a3 sqrt32 cdot frac16 3a2 cdot frac163a2 cdot frac163a2 20.endalignUsawa hutokea wakati frac3a3 sqrt32 frac163a2 na b fraca4. Tunaweza kutatua ili kupata a frac2sqrt3 na b frac12 sqrt3, kwa hivyo thamani ya chini ni 20. 