<prompt> Acha a, b, c iwe mizizi ya ujazo wa polinomia x3 - x - 1 0. Tafutaab - c2 bc - a2 ca - b2.  <response>: Kwa fomula za Vieta,anzaaligna b c 0, ab ac bc -1, abc 1.mwishoalignKishaanzaalignab - c2 bc - a2 ca - b2 ab2 - 2bc c2 bc2 - 2ac a 2 ca2 - 2ab b2 ab2 - 2abc ac2 bc2 - 2abc ba2 ca2 - 2abc cb2 ab2 - 2 ac2 bc2 - 2 ba2 ca2 - 2 cb2 ab2 ac2 bc2 ba2 ca2 cb2 - 6 a2 b c b2 a c c2 a b - 6.mwishoalignKutoka a b c 0, b c -a. Vile vile, a c -b na a b -c, hivyoa2 b c b2 a c c2 a b - 6 -a3 - b3 - c3 - 6.Tangu a ni mzizi wa x3 - x - 1 0, a3 - a - 1 0, hivyo -a3 -a - 1. Vile vile, -b3 -b - 1 na -c3 -c - 1, hivyoanzaalign-a3 - b3 - c3 - 6 -a - 1 -b - 1 -c - 1 - 6 -a b c - 9 -9.mwishopanga 