<prompt> Pata thamani ya chini yafracleft x dfrac1x kulia6 - kushoto x6 dfrac1x6 kulia - 2kushoto x dfrac1x kulia3 kushoto x3 dfrac1x3 kuliakwa x 0.  <response>: Hebufx fracleft x dfrac1x kulia6 - kushoto x6 dfrac1x6 kulia - 2kushoto x dfrac1x kulia3 kushoto x3 dfrac1x3 kulia.Tunaweza kuandikafx fracleft x dfrac1x kulia6 - kushoto x6 2 dfrac1x6 kulia kushoto x dfrac1x kulia3 kushoto x3 dfrac1x3 kulia fracleft x dfrac1x kulia6 - kushoto x3 dfrac1x3 kulia2kushoto x dfrac1 x kulia3 kushoto x3 dfrac1x3 kulia.Kwa tofauti ya miraba,anzaalignfx fracleft kushoto x dfrac1x kulia3 kushoto x3 dfrac1x3 kulia kulia kushoto kushoto x dfrac1x kulia3 - kushoto x3 dfrac1x3 kulia kulia kushoto x dfrac1x kulia3 kushoto x3 dfrac1x3 kulia kushoto x dfrac1x kulia3 - kushoto x3 dfrac1x3 kulia x3 3x frac3x frac1x3 - x3 - frac1x3 3x frac3x 3 kushoto x frac1x kulia.endalignNa AM-GM, x frac1x ge 2, sofx 3 kushoto x frac1x kulia ge 6.Usawa hutokea kwa x 1, hivyo thamani ya chini kabisa ya fx kwa x 0 ni 6. 