<prompt> Acha r_1, r_2, dots, r_7 ziwe mizizi changamano tofauti ya polynomial Px x7 - 7. HebuK prod_1 le i j le 7 r_i r_j.Kwa maneno mengine, K ni zao la nambari zote za fomu r_i r_j, ambapo i na j ni nambari kamili ambazo 1 le i j le 7. Determine K2.  <response>: Tunaweza kuandikax7 - 7 x - r_1x - r_2 dotsm x - r_7.Kubadilisha -x kwa x, tunapata-x7 - 7 -x - r_1-x - r_2 dotsm -x - r_7,hivyox7 7 x r_1x r_2 dotsm x r_7.Kuweka x r_i, tunapatar_i7 7 r_i r_1r_i r_2 dotsm r_i r_7.Kwa kuwa r_i ni mzizi wa x7 - 7, r_i7 7 . Kwa hiyo,r_i r_1r_i r_2 dotsm r_i r_7 14.Kuchukua bidhaa zaidi ya 1 le i le 7, tunapata2r_12r_2 dotsm 2r_7 K2 147.Kwa fomula za Vieta, r_1 r_2 dotsm r_7 7, hivyoK2 frac14727 cdot 7 76 117649. 