Sehloohong sena re tla leka tsebo ea lipalo ea ChatGPT. Re tla leka ho nka monyetla oa bohlale ba maiketsetso ho fumana mohlala o hanyetsanang le Theorem ea Motheo ea Algebra, ho fumana hore ntle le pelaelo e tla re tsebisa ho Medals ea Fields.
Haeba re botsa ka metso ea polynomial ea tekanyo ea 3, tabeng ena kaofela ke 'nete, ChatGPT e pheha khang ea hore qeto ea tlhahlobo e ka itšetleha ka polynomial e reriloeng, kahoo re khothalletsa ho sebelisa mokhoa oa ho pheta-pheta oa linomoro tse kang Newton-Raphson mokhoa.
Phoso palong ea motsoako
Ho fihlela joale, re ke ke ra belaella bokhoni ba lipalo ba AI, kahoo re ile ra leka ho rarolla bothata ba ho fumana metso ea polynomial p (x) = x3 - 3 × 2 + 4 mme re makatsoa ke hore e entse lipalo tse fosahetseng. ea derivative , kahoo ho fumana metso ha hoa nepahala. E khutlisa x = 0 joalo ka motso oa polynomial mme re e kopa ho e hlahloba. Ka tlhaho, e tseba ka boteng ba phoso empa ha e tsebe moo e etsahetseng teng. Re bone hore phoso e teng ho tsoa ho polynomial mme re kopa hore e baloe ho tloha metsong ka mokhoa oa Newton-Raphson. Hoa makatsa hore ebe e etsa phoso ea computational hape, lekhetlong lena ts'ebetsong e bonolo, joalo ka ha re bona setšoantšong se latelang:
Ho se bale hantle
Ha re hlokomela phoso ea lipalo, re mo botsa hape, re etsa phoso e 'ngoe, kahoo re mo fa phetetso ea pele ea Newton-Raphson Method, e leng, x₁ = 5/3 mme re kopa ho tsoela pele ho pheta-pheta, ho fella ka x₁ = 5 /3 ke motso oa polynomial. Re tiisa ka ho botsa hape hore na boleng ba 5/3 ke motso oa polynomial, 'me re fumana karabo e tiileng. Re kopa ho bala boleng ba polynomial ka boleng boo, 'me, kaha sephetho se fapane le zero, re se bontša hore e ke ke ea e-ba motso. Oa e utloisisa 'me o kōpa tšoarelo joalokaha re bona ka tlase:
Re etsa qeto ea hore khopolo ea Newton-Raphson Method e nepahetse, empa tšebeliso ea eona ha e joalo, kahoo re leka ho fumana metso ka mokhoa o mong, o kang oa factorization oa polynomial.
Tabeng ena, re fumana hore metso ea polynomial p(x) ke x = r le x = 1 ± 2i.
Ha u botsoa ho netefatsa hore boleng ba p(1+2i) ha se zero, kahoo e ke ke ea ba motso oa polynomial ea rona, amohela phoso hape. Ha re fihla boemong bona, re tsamaea ka leseli, 'me re mo bolella hore x = - 1 ke motso oa sebele oa polynomial le hore metso e meng kaofela e bala. Karabo ea hae ea pele e ne e ke ke ea re makatsa, e re bolella hore ho phaella ho x = - 1, metso e meng ea polynomial p(x)=4 - 3×2 + x3 ke x = 1 + 2i le x = 1 - 2i . Ho fihlela makhetlo a mane e fana ka liphetho tse fosahetseng hape, kahoo ha re na boikhethelo haese ho fana ka motso o mocha. Tabeng ena, ho e-na le ho fana ka eona, re botsa hore na x = 2 ke motso oa polynomial ea rona. Ikahlolele karabo, kapa ho e-na le hoo, lipalo tseo ChatGPT e li etsang ho hlahloba hore x = 2 ha se motso:
Kamora ho hlahloba lipalo tsa hau hape, qetella ka ho hlalosa hore metso ea polynomial ea rona ke x = – 1, x = 1, le x = 2.
Re tla u bontša hore metso eohle e meraro e khutlisa e nepahetseng, ke hore, x = 1 ha se motso ha tse ling tse peli li le joalo. Ha re tele mme re leka ho fumana motso oa boraro oa polynomial, 'me ke hona moo re fumanang tlhaloso e fosahetseng e kholo ka ho fetisisa. Litlhaloso tsa rōna: “Khopolo-taba ea Motheo ea Algebra e tiisa hore thuto e ’ngoe le e ’ngoe ea polynomial e na le metso hantle, ea sebele le e rarahaneng. Kahoo, haeba polynomial ea degree n e na le k metso ea 'nete, e tlameha ebe e na le metso e rarahaneng ea nk. Ho fihlela joale re lumellana. Re tsoela pele ka: “Tabeng ea polynomial p(x) = 4 – 3×2 + x3, re fumane hore e na le metso e ’meli ea sebele, x = – 1 le x = 2. Kaha p(x) ke polynomial ea degree 3, joale e tlameha ho ba le motso o eketsehileng o rarahaneng. Motso ona o rarahaneng ke x = 1 ± 2i.” Ha re khone ho tsoa ho makala a rona mme re nahana hore o ne a batla feela ho re bontša e 'ngoe ea metso e' meli, kahoo re mo fa monyetla o mong, o fellang ka:
Kahoo haeba re nepile, re sa tsoa fumana mohlala oa ho hanyetsa Theorem ea Motheo ea Algebra, polynomial ea degree 3 e nang le metso e 4. Na re mathela Medale oa Fields?
AI e netefalitse hore karabo ea hae e nepahetse ho fihlela makhetlo a mabeli hape, e bonts'a hore degree 3 polynomial e ka ba le metso e 4. Re bile re ikemiselitse ho li fumana re sebelisa Mokhoa oa Bisection. Joale ho joalo, re tlohela ho batla metso ea degree e bonolo ea 3 polynomial. Re lumelisa hantle ka pilisi ea ho qetela:
E le kakaretso ea ho qetela, ha re bolele hore ChatGPT ke Intelligence e mpe ea Maiketsetso, e hole le eona, haeba e se feela e fapaneng, e ntle haholo AI, empa ka boeona, ho Natural Language Processing, le hoja ho Mathematics e ntse e e-na le tsela e telele ea ho tsamaea. ithute. Re tlameha ho nyatsa liphetho tseo lienjine li khutlelang ho rona: ha se 'nete ho sa tsotellehe hore na li hlalositsoe hantle hakae,' me ho bonahala eka motho o haelloa ke ea ka netefatsang bonnete ba tsona.
MABAPI LE MONGOLI
Íñigo Sarría Martínez De Mendivil
Sengoliloeng sena se phatlalalitsoe qalong ho The Conversation.
