<prompt> Acha x na y ziwe nambari halisi chanya. Pata thamani ya chini yakushoto x frac1y kulia kushoto x frac1y - 2018 kulia kushoto y frac1x kulia kushoto y frac1x - 2018 kulia.  <response>: Na QM-AM,sqrtfracx frac1y2 y frac1x22 ge fracx frac1y y frac1x2,hivyokushoto x frac1y kulia2 kushoto y frac1x kulia2 ge frac12 kushoto x frac1y y frac1x kulia2.Kishaanzaalignkushoto x frac1y kulia kushoto x frac1y - 2018 kulia kushoto y frac1x kulia kushoto y frac1x - 2018 kulia kushoto x frac1y kulia2 kushoto y frac1x kulia2 - 2018 kushoto x frac1 y kulia - 2018 kushoto y frac1x kulia ge frac12 kushoto x frac1y y frac1x kulia2 - 2018 kushoto x frac 1y y frac1x kulia frac12 u2 - 2018u frac12 u - 20182 - 2036162,endalignambapo u x frac1y y frac1x.Usawa hutokea wakati u 2018 na x y. Hii ina maana x frac1x 1009, au x2 - 1009x 1 0. Tunaweza kuangalia kama hii quadratic ina mizizi halisi ambayo ni chanya, hivyo usawa unawezekana. Hivyo, thamani ya chini ni -2036162. 