<prompt> Acha z_1 na z_2 ziwe nambari mbili changamano kama vile z_1 5 nafracz_1z_2 fracz_2z_1 1.Tafuta z_1 - z_22.  <response>: Kutoka kwa mlinganyo fracz_1z_2 fracz_2z_1 1,z_12 z_22 z_1 z_2,hivyo z_12 - z_1 z_2 z_22 0. Kisha z_1 z_2z_12 - z_1 z_2 z_22 0, ambayo hupanuka kama z_13 z_23 0. Kwa hivyo, z_13 -z_23.Kuchukua thamani kamili ya pande zote mbili, tunapataz_13 z_23.Kisha z_13 z_23, hivyo z_2 z_1 5. Kisha z_1 overlinez_1 z_12 25, hivyo overlinez_1 frac25z_1. Vile vile, overlinez _2 frac25z_2.Sasa,anzaalignz_1 - z_22 z_1 - z_2 jumlaz_1 - z_2 z_1 - z_2 muhtasariz_1 - jumlaz_2 z_1 - z_2 kushoto frac25z_1 - frac25z_2 kulia 25 25 - 25 kushoto fracz_1z_2 fracz_2z_1 kulia 25 25 - 25 25.endalignMbadala: Tunakumbuka kuwa z_1 - z_2 z_1 cdot kushoto 1 - dfracz_2z_1 kulia.Acha u dfracz_2z_1, ili dfrac1u u 1, au u2 - u 1 0. Suluhu ni u dfrac1 pm sqrt-32 dfrac12 pm idfracsqrt32. Kishaanzaalignz_1 - z_22 z_12 cdot kushoto 1 - dfracz_2z_1 kulia2 52 cdot kushoto -dfrac12 mp idfracsqrt32 kulia2 25 cdot 1,endalignbila kujali ni thamani gani ya u tunayotumia. Kwa hiyo, z_1 - z_22 25. 