<prompt> Mlinganyo 2000x6100x510x3x-20una mizizi miwili halisi. Hesabu mraba wa tofauti kati yao.  <response>: Tunajaribu kuzingatia equation kipande kwa kipande. Anza na masharti 2000x6 na -2, na utumie tofauti ya cubes: anzailiyopangwa 2000x6 - 2 210x23 - 1 210x2-1100x4 10x2 1 20x2-2100x410x21. mwishozilizowianishwaSasa tunaona kwamba masharti yaliyosalia hufanya 100x5 10x3 x x100x4 10x2 1 100x5 100x4 10x2 1, ili tuweze kuainisha sehemu nzima ya kushoto- upande wa mkono, kutoa 20x2 x - 2100x4 10x2 1 0.Neno 100x4 10x2 1 daima ni chanya kwa halisi x, hivyo mizizi miwili halisi lazima iwe mizizi ya quadratic 20x2 x - 2 0. Kwa fomula ya quadratic, x frac-1 pm sqrt12 4cdot 2 cdot 2040 frac-1 pm sqrt161 40.Tofauti kati ya mizizi hii ni fracsqrt16120, kwa hivyo jibu ni frac161400. 