Kulesi sihloko sizohlola ulwazi lwezibalo lwe-ChatGPT. Sizozama ukusebenzisa ithuba lobuhlakani bokwenziwa ukuze sithole isibonelo esiphikisayo se-Fundamental Theorem ye-Algebra, sithola ukuthi ngokungangabazeki izosethula ekuqondeni i-Fields Medal.
Uma sibuza mayelana nezimpande ze-polynomial ye-degree 3, kulokhu konke okwangempela, i-ChatGPT ithi ukulungiswa kokuhlaziya kungase kuncike ku-polynomial ehlongozwayo, ngakho-ke sincoma ukusebenzisa indlela yezinombolo ephindaphindwayo njengendlela ye-Newton-Raphson.
Iphutha ekubalweni kokuphuma kokunye
Kuze kube manje, asikwazi ukungabaza ikhono lezibalo le-AI, ngakho-ke sazama ukuxazulula inkinga yokuthola izimpande ze-polynomial p(x) = x3 - 3×2 + 4 futhi ngokumangala kwethu yenza ukubala okungalungile. kokuphuma kokunye, ngakho ukuthola izimpande akulungile. Ibuyisela u-x = 0 njengempande ye-polynomial futhi siyicela ukuthi iyihlole. Ngokwemvelo, iyazi ngobukhona bephutha kodwa ayazi ukuthi yenzeke kuphi. Sibonile ukuthi iphutha liku-derivative ye-polynomial futhi sicela ukuthi ibalwe kusuka ezimpandeni ngokusebenzisa indlela ye-Newton-Raphson. Ngokumangalisayo, yenza iphutha lokubala futhi, kulokhu ekusebenzeni okulula, njengoba sibona esithombeni esilandelayo:
Ukubala okungalungile
Ngokubona iphutha ekubalweni, siyambuza futhi, senza elinye iphutha, ngakho-ke simnika ukuphindaphinda kokuqala kweNewton-Raphson Method, okungukuthi, x₁ = 5/3 futhi sicela ukuqhubeka nokuphindaphinda, okuholela ku-x₁ = 5 /3 iyimpande ye-polynomial. Siqinisekisa ngokubuza futhi ukuthi ingabe inani elingu-5/3 liyimpande ye-polynomial, futhi sithola impendulo eqinisekisayo. Sicela ukubala inani le-polynomial kulelo nani, futhi, njengoba umphumela uhlukile kunoziro, siyawubonisa ukuthi ayikwazi ukuba impande. Uyakuqonda futhi uyaxolisa njengoba sibona ngezansi:
Siphetha ngokuthi inkolelo-mbono ye-Newton-Raphson Method ilungile, kodwa ukusetshenziswa kwayo akunjalo, ngakho-ke sizama ukuthola izimpande sisebenzisa enye indlela, njenge-factorization ye-polynomial.
Kulesi simo, sithola ukuthi izimpande ze-polynomial p(x) zithi x = r kanye no-x = 1 ± 2i.
Uma ucelwa ukuthi uqinisekise ukuthi inani lika-p(1+2i) alilona uziro ngakho-ke alikwazi ukuba yimpande ye-polynomial yethu, phinda uvume iphutha. Ukufika kulesi simo, sihamba nenkomba, futhi simtshela ukuthi x = - 1 impande yangempela ye-polynomial nokuthi zonke ezinye izimpande zibala. Impendulo yakhe yokuqala ayizange isimangaze, isitshela ukuthi ngaphezu kuka x = – 1, ezinye izimpande ze-polynomial p(x)=4 – 3×2 + x3 zithi x = 1 + 2i kanye no x = 1 – 2i . Kuze kube izikhathi ezine inikeza imiphumela engalungile futhi, ngakho-ke asinakho ukukhetha ngaphandle kokuyinikeza impande entsha. Kulokhu, esikhundleni sokukunikeza, siyabuza ukuthi x = 2 iyimpande ye-polynomial yethu. Zinqumele wena impendulo, noma kunalokho, izibalo ezenziwa yi-ChatGPT ukuze uhlole ukuthi x = 2 akuyona impande:
Ngemva kokuhlola izibalo zakho futhi, qedela ngokuchaza ukuthi izimpande ze-polynomial yethu zithi x = – 1, x = 1, kanye no-x = 2.
Sizokukhombisa ukuthi zontathu izimpande, zibuyisela okulungile, okungukuthi, x = 1 akuyona impande ngenkathi amanye amanani amabili eyimpande. Asiyeki futhi sizame ukuthola umsuka wesithathu we-polynomial, futhi yilapho kanye sithola khona ukuhunyushwa okuyiphutha okukhulu. Izincazelo zethu: “I-Fundamental Theorem ye-Algebra iqinisekisa ukuthi yonke i-polynomial of degree inezimpande n ncamashi, kokubili okwangempela neziyinkimbinkimbi. Ngakho-ke, uma i-polynomial ye-degree n inezimpande zangempela zika-k, kufanele ibe nezimpande eziyinkimbinkimbi ze-nk. Kuze kube manje siyavumelana. Siqhubeka ngokuthi: “Endabeni ye-polynomial p(x) = 4 – 3×2 + x3, sithole ukuthi inezimpande ezimbili zangempela, x = – 1 kanye no x = 2. Njengoba p(x) i-polynomial ye-degree 3, ngakho-ke kufanele ibe nempande eyinkimbinkimbi eyengeziwe. Lempande eyinkimbinkimbi ithi x = 1 ± 2i.” Asikwazi ukuphuma ekumangaleni kwethu futhi sicabanga ukuthi ubefuna ukusikhombisa izimpande ezimbili kuphela, ngakho simnika elinye ithuba, okuholela kulokhu:
Ngakho-ke uma siqinisile, sisanda kuthola isibonelo esiphikisayo ku-Fundamental Theorem of Algebra, i-polynomial yedigri 3 enezimpande ezi-4. Ingabe sigijimela i-Fields Medal?
I-AI iphinde yaqinisekisa ukuthi impendulo yakhe ilungile kuze kube izikhathi ezimbili ngaphezulu, okubonisa ukuthi idigri 3 polynomial ingaba nezimpande ezi-4. Saze sazimisela ukubathola sisebenzisa i-Bisection Method. Manje yebo, siyayeka ukufuna izimpande ze-degree 3 polynomial elula. Sivalelisa kahle ngephilisi elilodwa lokugcina:
Njengesifinyezo sokugcina, asisho ukuthi i-ChatGPT iyi-Artificial Intelligence embi, kude nayo, uma kungenjalo nje okuphambene, i-AI enhle kakhulu, kodwa ngokwayo, ku-Natural Language Processing, nakuba ku-Mathematics isenayo. indlela ende okufanele uyihambe. funda. Kufanele sigxeke imiphumela ezibuyiselwa izinjini kithina: azilona iqiniso noma ngabe zichazwe kahle kangakanani, futhi kubukeka sengathi umuntu ulahlekile ongaqinisekisa ubuqiniso bazo.
MAYELANA NOMBHALI
U-Íñigo Sarría Martínez De Mendivil
Lesi sihloko sishicilelwe ekuqaleni kwethi Ingxoxo.
