<prompt> Acha x_1, x_2, dots , x_6 ziwe nambari halisi zisizo hasi kama vile x_1 x_2 x_3 x_4 x_5 x_6 1, na x_1 x_3 x_5 x_2 x_4 x_6 ge frac1 540. Pata thamani ya juu zaidi yax_1 x_2 x_3 x_2 x_3 x_4 x_3 x_4 x_5 x_4 x_5 x_6 x_5 x_6 x_1 x_6 x_1 x_2.  <response>: Acha a x_1 x_3 x_5 x_2 x_4 x_6 na b x_1 x_2 x_3 x_2 x_3 x_4 x_3 x_4 x_5 x_4 x_5 x_6 x_5 x_6 x_1 x_6 x_1 x_2. By AM-GM,a b x_1 x_4x_2 x_5x_3 x_6 le kushoto fracx_1 x_4 x_2 x_5 x_3 x_63 kulia3 frac127.Kwa hiyo,b le frac127 - frac1540 frac19540.Usawa hutokea ikiwa na iwapo tux_1 x_4 x_2 x_5 x_3 x_6.Pia tunataka a frac1540 na b frac19540. Kwa mfano, tunaweza chukua x_1 x_3 frac310, x_5 frac160, x_2 frac13 - x_5 frac1960 , x_4 frac13 - x_1 frac130, na x_6 frac13 - x_3 frac130 .Kwa hivyo, thamani ya juu zaidi ya b ni frac19540. 