<prompt> Acha m iwe suluhisho kubwa zaidi la mlinganyodfrac3x-3 dfrac5x-5 dfrac17x-17 dfrac19x-19 x2 - 11x - 4Kuna nambari kamili chanya a, b, na c kiasi kwamba m a sqrtb sqrtc. Tafuta abc.  <response>: Tunaongeza 4 kwa pande zote mbilikushoto1dfrac3x-3kulia kushoto1dfrac5x-5kulia kushoto1 dfrac17 x-17 kulia kushoto1dfrac19x-19kulia x2 - 11x au fracxx-3 fracxx-5 fracxx-17 fracxx-19 x2-11x.Ama x0, au frac1x-3 frac1x-5 frac1x-17 frac1x-19 x-11. Ili kushawishi ulinganifu fulani, tunakokotoa kwamba wastani wa nambari x-3, x-5, x-17, x-19 ni x-11. Kisha, tukiruhusu t x-11, tuna frac1t8 frac1t6 frac1t-6 frac 1t-8 t,au, ukichanganya istilahi ya kwanza na ya mwisho na istilahi ya pili na ya tatu, frac2tt2-64 frac2tt 2-36 t.Ama t0, au tunaweza kugawanya kwa t na kuzidisha, tukitoa 2t2-36 2t2-64 t2-36t2-64 inamaanisha 0 t4 - 104t2 2504.Kukamilisha mraba, tunapata t2-522 200 , kwa hivyo t2 52 pm sqrt200, na t pm sqrt52 pm sqrt200. Inatengua ubadilishaji t x-11, tuna x 11 pm sqrt52 pm sqrt200.Kwa hivyo, mzizi mkubwa zaidi ni x 11sqrt52 sqrt200 ambayo ni kubwa kuliko zote x0 na t0 inamaanisha x11, na jibu ni 11 52 200 263. 