Theorem Vieta kunye nentwana imbali

Vieta theorem - ligama eliqhelekileyo esikolweni phantse wonke umntu. Kodwa ingaba "esiqhelekileyo" ngokwenene? Bambalwa sihlangana nabo kubomi bemihla ngemihla. Kodwa asingabo bonke abo sisebenzisana kwimathematika, maxa wambi ukuqonda ngokupheleleyo intsingiselo enzulu nokubaluleka enkulu yale theorem.

Vieta theorem lula kakhulu inkqubo yokusombulula inani elikhulu iingxaki zezibalo, nto leyo ekugqibeleni ubilisa phantsi yokusombulula i'quadratic equation :

ax2 + 'bx' + c = 0, apho ≠ 0.

Olu hlobo umgangatho i'quadratic equation. Kwiimeko ezininzi, i'quadratic equation onjalo uye okuza a, b, c, nabanako lula lula ngokwahlula ukuba ibe. Kulo mzekelo, sifika imin kwe quadratic equation, ekuthiwa imadlana (xa inani lokuqala lenxaki ilingana no-1):

x2 + px + q = 0

Kungenxa olu hlobo zibalo kwaye lula ukusebenzisa theorem ka Vieta. Into theorem ephambili kukuba amaxabiso esineengcambu kv.uravneniya enikwa ngomlomo kube lula ezimiselwe ukwazi ngokunxulumene esisiseko theorem:

• sum of kweengcambu lilingana nenani lomlingani malunga yesibini (ngamanye amazwi, -p);
• imveliso ilingana umba lesithathu (oko kukuthi, q).

Ezizezi, x1 + x2 = -p, kunye x1 * x2 = q.

Isigqibo sesininzi iingxaki kwimathematika kwisikolo kuyehla kube ipere elula lwamanani ukuba kulula ukufumana kwi ilifa izakhono ubuncinane ukubala ngomlomo. Kwaye ukuba kunokubangela naziphi na iingxaki. Kukho theorem uguqulo Vieta ivumela isibini ekhoyo amanani, zona iingcambu quadratic equation ', kulula ukubuyisela okuza yawo kwaye uyibhale ngendlela eqhelekileyo.

Ukukwazi ukusebenzisa Vieta theorem njengesixhobo becala ngokuzithomalalisa iingxaki zemathematika ngokwasemzimbeni ebudeni kwisikolo samabanga aphakamileyo. Ingakumbi eli khono buyafuneka ekulungiseleleni abafundi of kwiiklasi zabafundi abadala ukwenzela uviwo.

Eqonda ukubaluleka isixhobo lweMathematika elula nesebenzayo, andinako ukunceda ukucinga umntu, okokuqala kokuba kuvulwa.

Fransua Viet - nesazi-nzulu esidumileyo French, lowo waqala umsebenzi igqwetha. Kodwa ke, ngokuqinisekileyo, imathematika ubizo lwakhe. Nangona kwinkonzo yasebukhosini njengomcebisi, waba edumileyo, wakwazi ukufunda ingenelelwe umyalezo khowudi ye uKumkani eSpeyin eNetherlands. Oku wanika French ukumkani Henry III ithuba lokuba ukwazi yonke iminkqangiyelo abachasi bakhe.

Ngokuthe ngcembe, njengentshayelelo iimbalo, Fransua Viet weza kwisigqibo sokuba kufuneka kubekho unxulumano olusondeleleneyo phakathi Kwemithetho Yokwenziwa zakutshanje ngelo xesha uphando 'algebraists "kunye nelifa enzulu zejometri yamandulo. Ekuhambeni yophando lwenzululwazi kwathiwa yenzelwe yaye zakhiwe phantse yonke algebra aphantsi. Yena kuqala yaqalisa ukusetyenziswa amaxabiso yokoqobo izixhobo zemathematika, umahluko ocacileyo phakathi ingqiqo lwenani, kunye nexabiso ulwalamano lwabo. Wyeth wabonisa ukuba lokuqhuba imisebenzi ngendlela yokomfuziselo, nako ukusombulula ingxaki kwimeko jikelele, phantse onke amaxabiso amaxabiso ekhankanyiweyo.

Uphando lwakhe zokusombulula zibalo ngaphezu yesibini, neziphumo theorem ngoku eyaziwa ngokuba ngokubanzi theorem of Vieta. Kuye ziyakubaluleka enkulu, yaye isicelo yayo yenza isicombululo ekhawulezayo ukuya quadratic komyalelo eliphezulu.

Enye iimpawu le theorem na ngolu hlobo lulandelayo: udibaniso lwamaxabiso wonke iingcambu weqondo n-th ilingana kumalungu ayo simahla. Le impahla isoloko isetyenziswa ekusombululeni zibalo of lesithathu okanye lesine ngenjongo yokunciphisa ngokomyalelo polynomial. Ukuba isidanga polynomial n-th na iingcambu inani elipheleleyo, ukuba kube lula ezichongwe yi ukhetho elula. Koko, ngokwenza ukwahlulwa polynomial kwi ibinzana (x1-x), indawo polynomial (n-1) th isidanga.

Ekugqibeleni, siphawula ukuba theorem Vieta yenye khosi algebra theorems zesikolo idumileyo. Kwaye igama lakhe kuthatha indawo ufanelwe phakathi amagama zezibalo enkulu.