<prompt> Acha z_1, z_2, z_3 ziwe nambari changamano kiasi kwamba z_1 1,z_2 2,z_3 3, na9z_1 z_2 4z_1 z_3 z_2 z_3 12.Tafuta z_1 z_2 z_3.  <response>: Kwa kuwa nambari changamano na muungano wake huwa na ukubwa sawa kila wakati,jumla9z_1 z_2 4z_1 z_3 z_2 z_3 9 umuhimuz_1 ujumlaz_2 4 ujumlaz_1 ujumlaz_3 ujumlaz_2 ujumlaz_3 12.Kutoka kwa maelezo uliyopewa, z_1 overlinez_1 z_12 1, hivyo overlinez_1 frac1z_1. Vile vile, overlinez_2 frac4z_2 quad textna quad overlinez_3 frac9z_3,hivyoanzaalign9 muhtasariz_1 ujumlaz_2 4 ujumlaz_1 ujumlaz_3 ujumlaz_2 ujumlaz_3 kushoto 9 cdot frac1z_1 cdot frac4z_2 4 cdot frac1z_1 cdot frac9z_3 frac4101 z_2 cdot frac9z_3 kulia kushoto frac36z_1 z_2 frac36z_1 z_3 frac36z_2 z_3 kulia frac36z_1 z_2 z_3 z_1 z_2 z_3 frac361 cdot 2 cdot 3 z_1 z_2 z_3 6 z_1 z_2 z_3.endalignLakini idadi hii pia ni 12, kwa hivyo z_1 z_2 z_3 2. 