<prompt> Acha a, b, c, d ziwe nambari halisi, ambazo hakuna ambazo ni sawa na -1, na omega iwe nambari changamano kiasi kwamba omega3 1 na omega neq 1. Kamafrac1a omega frac1b omega frac1c omega frac1d omega frac2omega,kisha tafutafrac1a 1 frac1b 1 frac1c 1 frac1d 1.  <response>: Kwa kuwa omega3 1, frac2omega 2 omega2. Kisha kuzidisha pande zote mbili kwa a omegab omegac omegad omega, tunapatab omegac omegad omega a omegac omegad omega a omegab omegad omega a omegab omegac omega 2 omega2 a omegab omegac omega d omega.Kupanua pande zote mbili, tunapataanzaalign4 omega3 3a b c d omega2 2ab ac ad bc bd cd omega abc abd acd bcd 2 omega6 2a b c d omega5 2ab ac ad bc bd cd omega4 2abc abd acd bcd omega3 2abcd omega2.endalignKwa kuwa omega3 1, hii hurahisishaanzaalign3a b c d omega2 2ab ac ad bc bd cd omega abc abd acd bcd 4 2a b c d 2abcd omega2 2ab ac ad bc bd cd omega 2abc abd acd bcd 2 .mwishoalignKishaa b c d - 2abcd omega2 - abc - abd - acd - bcd 2 0.Kwa kuwa omega2 si halisi, ni lazima tuwe na a b c d 2abcd. Kisha abc abd acd bcd 2.Kwa hivyo,anzaalignfrac1a 1 frac1b 1 frac1c 1 frac1d 1 fracb 1c 1d 1 a 1c 1d 1 a 1b 1d 1 a 1b 1c 1a 1b 1c 1d 1 fracabc abd acd bcd 2ab ac ad bc bd cd 3a b c d 4abcd abc abd acd bcd ab ac ad bc bd cd a b c d 1 frac2 2ab ac ad bc bd cd 6abcd 4abcd 2 ab ac ad bc bd cd 2abcd 1 frac6abcd 2ab ac ad bc bd cd 63abcd ab ac ad bc bd cd 3 2.mwishopanga 