<prompt> Acha a, b, c ziwe nambari halisi kiasi kwamba 1 le a le b le c le 4. Pata thamani ya chini zaidi yaa - 12 kushoto fracba - 1 kulia2 kushoto fraccb - 1 kulia2 kushoto frac4c - 1 kulia2.  <response>: Na QM-AM,anzaalignsqrtfraca - 12 fracba - 12 fraccb - 12 frac4 c - 124 ge fraca - 1 fracba - 1 fraccb - 1 frac4c - 14 fraca fracba fraccb frac4c - 44.mwishoalignNa AM-GM,a fracba fraccb frac4c ge 4 sqrt44 4 sqrt2, hivyosqrtfraca - 12 fracba - 12 fraccb - 12 frac 4c - 124 ge sqrt2 - 1,naa - 12 kushoto fracba - 1 kulia2 kushoto fraccb - 1 kulia2 kushoto frac4c - 1 kulia2 ge 4 sqrt2 - 12 12 - 8 sqrt2.Usawa hutokea wakati a sqrt 2, b 2, na c 2 sqrt2, kwa hivyo thamani ya chini ni 12 - 8 sqrt2. 