<prompt> Acha x, y, z ziwe nambari halisi zisizo hasi. HebuanzaalignA sqrtx 2 sqrty 5 sqrtz 10, B sqrtx 1 sqrty 1 sqrtz 1.endalignTafuta thamani ya chini kabisa ya A2 - B2.  <response>: Tunaweza kuandikaanzaalignA2 - B2 A BA - B sqrtx 2 sqrtx 1 sqrty 5 sqrty 1 sqrtz 10 sqrtz 1 quad nyakati sqrtx 2 - sqrtx 1 sqrty 5 - sqrty 1 sqrtz 10 - sqrtz 1.mwishoalignHebuanzaaligna_1 sqrtx 2 sqrtx 1, b_1 sqrty 5 sqrty 1, c_1 sqrtz 10 sqrtz 1, a_2 sqrtx 2 - sqrtx 1, b_2 sqrty 5 - sqrty 1, c_2 sqrtz 10 - sqrtz 1.endalignKisha kwa Cauchy-Schwarz,anzaalignA2 - B2 a_1 b_1 c_1a_2 b_2 c_2 ge sqrta_1 a_2 sqrtb_1 b_2 sqrtc_2 c_22 1 2 32 36.endalignUsawa hutokea wakatifraca_1a_2 fracb_1b_2 fracc_1c_2,au kwa usawa,fracx 2x 1 fracy 5y 1 fracz 10z 1.Kwa mfano, ikiwa tutaweka kila moja. sehemu hadi 2, kisha tunapata x 0, y 3, na z 8.Kwa hivyo, thamani ya chini ni 36. 