<prompt> Acha x_1, x_2, x_3, dots, x_100 ziwe nambari halisi chanya kama x_12 x_22 x_32 dots x_100 2 1. Pata thamani ya chini zaidi yafracx_11 - x_12 fracx_21 - x_22 fracx_31 - x_32 dots fracx_100 1 - x_1002.  <response>: Kumbuka kuwa x_i 1 kwa i. zoteTunadai hivyofracx1 - x2 ge frac3 sqrt32 x2kwa 0 zote x 1. Hii ni sawa na 2x ge 3 sqrt3 x2 1 - x2 3x2 sqrt3 - 3x4 sqrt3, au3 sqrt3 x4 - 3x2 sqrt3 2x ge 0.Tunaweza kubainisha hili kamax x sqrt3 - 12 x sqrt3 2 ge 0,ambayo inashikilia kwa uwazi. Hivyo,fracx1 - x2 ge frac3 sqrt32 x2.Inafuata kwambafracx_11 - x_12 fracx_21 - x_22 fracx_31 - x_32 dots fracx_100 1 - x_1002 ge frac3 sqrt32 x_12 x_22 x_32 vitone x_1002 frac3 sqrt32.Usawa hutokea wakati x_1 x_2 x_3 frac1sqrt3 na x_4 x_5 dots x_ 100 0, kwa hivyo thamani ya chini ni frac3 sqrt32. 