Thiab qhov kev xav tsis thoob vim li cas qhov kev sib npaug qib tsib tsis tuaj yeem daws tau yog tias tsis muaj qhov sib luag ntawm plaub lub luag haujlwm hauv A, B, C, D, thiab E uas tau khaws cia raws li kev hloov pauv ntawm tsib ntawv.
Yuav ua li cas quintic tsis muaj pes tsawg tiag?
A polynomial muaj nuj nqi yuav muaj ntau, ib qho, lossis tsis muaj xoom. … Txawm hais tias khib los yog txawm, ib tug polynomial ntawm qhov kev txiav txim zoo tuaj yeem muaj tus lej ntau tshaj plaws sib npaug rau nws qhov kev txiav txim. Piv txwv li, lub cubic muaj nuj nqi tuaj yeem muaj ntau li peb xoom, tab sis tsis muaj ntxiv. Qhov no yog lub npe hu ua lub hauv paus theorem ntawm algebra.
Yuav ua li cas quintic equations daws tau?
Tsis zoo li plaub npaug, cubic, thiab quartic polynomials, general quintic tsis tuaj yeem daws cov lej hauv cov ntsiab lus ntawm tus lej kawg ntawm kev ntxiv, rho tawm, sib npaug, faib, thiab cov hauv paus extractions, raws li kev ua kom pom tseeb los ntawm Abel (Abel's impossibility theorem) thiab Galois.
Vim li cas thiaj tsis muaj quartic formula?
Yog, muaj cov mis quartic. Tsis muaj kev daws teeb meem los ntawm radicals rau qib siab dua. Qhov no yog qhov tshwm sim ntawm Galois txoj kev xav, thiab ua raws li qhov tseeb tias pawg symmetric S5 tsis tuaj yeem daws tau. Nws hu ua Abel's theorem.
Yuav ua li cas txhua qhov kev sib npaug thib tsib tuaj yeem daws tau los ntawm cov radicals?
yog qhov kev sib npaug yooj yim tshaj plaws uas tsis tuaj yeem daws tau hauv cov radicals, thiab yuav luag tag nrho cov polynomials ntawm qib tsib lossis siab dua tsis tuaj yeem daws tau hauv radicals.
