<prompt> Acha a,b, c iwe mizizi yax3 - 6x2 3x 1 0.Tafuta thamani zote zinazowezekana za a2 b b2 c c2 a. Ingiza thamani zote zinazowezekana, zikitenganishwa na koma.  <response>: Kwa fomula za Vieta,anzaaligna b c 6, ab ac bc 3, abc -1.endalignHebu p a2 b b2 c c2 a na q ab2 bc2 ca2. Kishap q a2 b ab2 a2 c ac2 b2 c bc2.Kumbuka kwambaa b cab ac bc a2 b ab2 a2 c ac2 b2 c bc2 3abc,hivyoanzaaligna2 b ab2 a2 c ac2 b2 c bc2 a b cab ac bc - 3abc 63 - 3-1 21.mwishoalignPia,pq a3 b3 a3 c3 b3 c3 a4 bc ab4 c abc4 3a2 b2 c2. Ili kupata masharti a3 b3 a3 c3 b3 c3, tunaweza mchemraba ab ac bc:anzaalignab ac bc3 a3 b3 a3 c3 b3 c3 quad 3a3 b2 c a3 bc2 a2 b3 c a2 bc3 ab3 c2 ab2 c3 quad 6a2 b2 c2.mwishoalignSasa,anzaaligna3 b2 c a3 bc2 a2 b3 c a2 bc3 ab3 c2 ab2 c3 abc a2 b ab2 a2 c ac2 b2 c bc2 -121 -21,mwishoalignhivyoanzaaligna3 b3 a3 c3 b3 c3 ab ac bc3 - 3-21 - 6a2 b2 c2 33 - 3-21 - 6-12 84.mwishoalignPia,a4 bc ab4 c abc4 abca3 b3 c3.Ili kupata masharti a3 b3 c3, tunaweza kufanya mchemraba a b c:a b c3 a3 b3 c3 3a2 b ab2 a2 c ac2 b2 c bc 2 6abc,hivyoanzaaligna3 b3 c3 a b c3 - 3a2 b ab2 a2 c ac2 b2 c bc 2 - 6abc 63 - 321 - 6-1 159.mwishoalignKwa hiyo,anzaalignpq a3 b3 a3 c3 b3 c3 a4 bc ab4 c abc4 3a2 b2 c2 84 -1 159 3-12 -72.endalignKisha kwa fomula za Vieta, p na q ndio mizizi yax2 - 21x - 72 x - 24x 3 0.Kwa hivyo, thamani zinazowezekana za p na q ni 24,-3. 