<prompt> Acha x_1, x_2, dots, x_101 ziwe nambari halisi chanya kama vile x_12 x_22 dots x_1012 1. Pata thamani ya juu yax_1 x_2 x_1 x_3 vitone x_1 x_101.  <response>: Na ukosefu wa usawa wa AM-QM,fracx_2 x_3 vitone x_101100 le sqrtfracx_22 x_32 vitone x_1012100 .Kisha x_2 x_3 vitone x_101 le 10 sqrtx_22 x_32 vitone x_1012, hivyox_1 x_2 x_1 x_3 vitone x_1 x_101 le 10x_1 sqrtx_22 x_32 vitone x_1012 10x_1 sqrt1 - x_12 .Kwa ukosefu wa usawa wa AM-GM,x_1 sqrt1 - x_12 le fracx_12 1 - x_122 frac12,hivyo 10x_1 sqrt 1 - x_12 le 5.Usawa hutokea wakati x_1 frac1sqrt2 na x_2 x_3 dots x_101 frac110 sqrt2, hivyo thamani ya juu ni 5. 