<prompt> Acha x na y ziwe nambari halisi chanya. Pata thamani ya chini yafracsqrtx2 y23x2 y2xy.  <response>: Na Cauchy-Schwarz,y2 x23x2 y2 ge xy sqrt3 xy2,hivyofracsqrtx2 y23x2 y2xy ge 1 sqrt3. Usawa hutokea wakati frac y23x2 fracx2y2, au y x sqrt43, hivyo thamani ya chini ni 1 sqrt3 . 