<prompt> Acha x, y, z ziwe nambari halisi ili -1 x, y, z 1. Pata thamani ya chini zaidi yafrac11 - x1 - y1 - z frac11 x1 y1 z.  <response>: Kuweka kila kitu juu ya dhehebu la kawaida, tunapataanzaalignfrac11 - x1 - y1 - z frac11 x1 y1 z frac 1 x1 y1 z 1 - x1 - y1 - z1 - x1 - y1 - z1 x1 y1 z frac2 2xy xz yz1 - x21 - y21 - z2.endalignKumbuka kwamba 2 2xy xz yz ge 2 na 1 - x21 - y21 - z2 le 1, hivyofrac2 2xy xz yz1 - x21 - y21 - z2 ge 2. Usawa hutokea wakati x y z 0, hivyo thamani ya chini ni 2. 