<prompt> Acha x_1,y_1, x_2,y_2, dots, x_n,y_n ziwe jozi x,y zilizoagizwa za nambari halisi kama vile xy 2 na x5y582. Tafutax_12 y_12 x_22 y_22 vitone x_n2 y_n2.  <response>: Kwa kuwa x y 2, kuna nambari halisi t vile x 1 t na y 1 - t. Kisha1 t5 1 - t5 82.Hii hurahisisha hadi 10t4 20t2 - 80 0. Mlinganyo huu unatokana na 10t2 - 2 t2 4 0, hivyo t pm sqrt2.Kwa hivyo, suluhu ni 1 sqrt2, 1 - sqrt2 na 1 - sqrt2, 1 sqrt2, na jibu la mwisho ni1 sqrt22 1 - sqrt22 1 - sqrt22 1 sqrt22 12. 