<prompt> Acha a, b, c ziwe nambari halisi chanya. Pata thamani ya chini yakushoto 2a frac13b kulia2 kushoto 2b frac13c kulia2 kushoto 2c frac1 3a kulia2.  <response>: Kupanua, tunapatakushoto 2a frac13b kulia2 kushoto 2b frac13c kulia2 kushoto 2c frac1 3a kulia2 4a2 frac4a3b frac19c2 4b2 frac4b3c frac1 9c2 4c2 frac4c3a frac19a2.Na AM-GM, 4a2 frac19c2 4b2 frac19c2 4c2 frac19a2 ge 6 sqrt64a2 cdot frac19c2 cdot 4b2 cdot frac19c2 cdot 4c2 cdot frac1 9a2 4nafrac4a3b frac4b3c frac4c3a ge 3 sqrt3frac4a3b cdot frac 4b3c cdot frac4c3a 4.Kwa hiyo,4a2 frac4a3b frac19c2 4b2 frac4b3c frac19c2 4c2 frac4c3a frac19a2 ge 8. Usawa hutokea wakati 2a 2b 2c frac13a frac 13b frac13c na frac4a3b frac4b3c frac4c3a, au a b c frac1sqrt6, hivyo thamani ya chini ni 8. 