<prompt> Tafuta idadi ya suluhisho za kwelix2006 1x2004 x2002 x2000 dots x2 1 2006x2005.  <response>: Kumbuka kuwa x 0 sio suluhisho. Pia, ikiwa x 0, basi upande wa kushoto ni chanya na upande wa kulia ni hasi, kwa hivyo x haiwezi kuwa suluhu. Hivyo, mizizi yoyote halisi lazima iwe chanya. Chukulia x 0.Kugawanya pande zote mbili kwa x2005, tunapatafracx2006 1x2004 x2002 x2000 dots x2 1x2005 2006.Kishafracx2006 1x1003 cdot fracx2004 x2002 x2000 dots x2 1x1002 2006,aukushoto x1003 frac1x1003 kulia kushoto x1002 x1000 x998 vitone frac1x998 frac1x1000 frac1x1002 kulia 2006.Na AM-GM ,anzaalign x1003 frac1x1003 ge 2, x1002 x1000 x998 vitone frac1x998 frac1x1000 frac 1x1002 ge sqrt1003x1002 cdot x1000 cdot x998 dotsm frac1x998 cdot frac1x1000 cdot frac1x1002 1003,mwishoalignhivyokushoto x1003 frac1x1003 kulia kushoto x1002 x1000 x998 vitone frac1x998 frac1x1000 frac1x1002 kulia ge 2006.Kwa vile tuna kesi ya usawa, thamani pekee inayowezekana ya x ni 1, kwa hivyo kuna 1 mzizi halisi. 