<prompt> Acha a, b, c ziwe nambari kamili tofauti, na omega iwe nambari changamano kiasi kwamba omega3 1 na omega neq 1. Tafuta thamani ndogo iwezekanavyo. yaa b omega c omega2.  <response>: Kumbuka kuwa omega3 omega3 1, hivyo omega 1. Kisha omega overlineomega omega2 1.Pia, omega3 - 1 0, ambayo huchangia kama omega - 1omega2 omega 1 0. Tangu omega neq 1,omega2 omega 1 0.Kwa hiyo,anzaaligna b omega c omega22 a b omega c omega2a b jumlaomega c jumlaomega2 a b omega c omega2 kushoto a fracbomega fraccomega2 kulia a b omega c omega2a b omega2 c omega a2 b2 c2 omega omega2 ab omega omega2 ac omega2 omega4 bc a2 b2 c2 omega omega2 ab omega omega2 ac omega omega2 bc a2 b2 c2 - ab - ac - bc fraca - b2 a - c2 b - c22.endalignKwa kuwa a, b, na c ni tofauti, zote tatu za a - b, a - c, na b - c lazima iwe angalau 1, na angalau moja ya maadili haya kamili lazima iwe angalau 2, hivyofraca - b2 a - c2 b - c22 ge frac1 1 42 3. Usawa hutokea wakati a,b, na c ni nambari tatu zinazofuatana, kwa mpangilio wowote, kwa hivyo thamani ndogo kabisa ya a b omega c omega2 ni sqrt3. 