Vieta ta Theorem kuma a bit na tarihi

Vieta Theorem - wani ra'ayi saba daga makaranta kusan kowa da kowa. Amma ko da shi ne "saba" da gaske? 'Yan ci karo da su a cikin rayuwar yau da kullum. Amma ba dukan waɗanda ake tafiyad da lissafi, wani lokacin sun fahimci zurfin ma'anar da kuma bayar da muhimmanci na wannan Theorem.

Vieta Theorem ƙwarai simplifies kan aiwatar da warware wata babbar dama ilmin lissafi matsaloli, abin da kyakkyawan tafasa saukar zuwa warware wani quadratic lissafi :

ax2 + bx + c = 0, inda wani ≠ 0.

Wannan shi ne misali irin na quadratic lissafi. A mafi yawan lokuta, irin wannan quadratic lissafi ya coefficients a, b, c kuma, wanda za a iya readily Sauki ta rarraba su a cikin wani. A wannan yanayin, muna zo a ma'anar da quadratic lissafi, da ake kira rage (lõkacin da farko coefficient na lissafi ne daidai da 1):

x2 + px + q = 0

Yana da ga irin wannan lissafai da kuma dace don amfani da Theorem na Vieta. Babban ji Theorem ne cewa dabi'u na tushen kv.uravneniya ba da baki za a iya sauƙi ƙaddara da sanin ainihin aboki na Theorem:

• Naira Miliyan Xari da tushen ne daidai da adadin m biyu coefficient (Ina nufin, -p).
• samfurin ne daidai da uku factor (ie, q).

Wato, x1 + x2 = -p, kuma x1 * x2 = q.

Da shawarar da mafi yawan matsaloli a makaranta lissafi an rage zuwa sauki biyu daga lambobin da suke da sauki a samu a} alla basira mallaki baka lissãfi. Kuma shi ya kamata ba sa wani matsaloli. Akwai wani kishiya Theorem na Vieta damar domin data kasance biyu daga lambobi, wanda su ne tushen wata quadratic lissafi, shi ne mai sauki mayar da coefficients da kuma rubuta a misali form.

Ability don amfani da Vieta Theorem a matsayin kayan aiki sun fi mayar da alleviates ilmin lissafin da kuma ta jiki da matsaloli a cikin shakka daga makarantar sakandare. Musamman wannan fasaha ne ba makawa a shirya dalibai na babban jami'in azuzuwan ga jarrabawa.

Farga da muhimmancin irin wannan mai sauki da kuma tasiri ilmin lissafi kayan aiki, da zan iya ba taimake tunanin wani mutum, karo na farko shi ne ya bude.

Fransua việt - sanannen Faransa masanin kimiyya, wanda ya fara aiki a matsayin lauya. Amma, a fili, ilmin lissafi shi ne ya kira. Duk da yake sarauta sabis kamar yadda mai ba da shawara, ya zama shahararren, ya ya iya karanta wani intercepted masu lamba sako na Sarkin Spain da Netherlands. Wannan ya ba da Faransa sarki Henry III da damar sani game da duk nufi da abokan adawarsa.

A hankali, wani gabatarwar to ilmin lissafi ilimi, Fransua việt zo ga ƙarshe cewa akwai dole ne a kusa da alaka tsakanin latest a lokacin gudanar da bincike "algebraists" da kuma zurfin al'adunmu na zamanin d lissafi. A cikin shakka daga kimiyya bincike da aka tsara da kuma tsara ta kusan duk na farko aljabara. Ya fara gabatar da yin amfani da zahiri dabi'u a cikin ilmin lissafi na'ura, da bambanci a fili tsakanin manufar lamba, da darajar da dangantaka. Wyeth ya nuna cewa ta hanyar aikata ayyukan a wani m tsari, zai iya magance matsalar a general hali, domin kusan duk dabi'u na kayyade dabi'u.

Da bincike domin warware lissafai fiye da na biyu, sa a Theorem wanda yanzu aka fi sani da jimlace Theorem na Vieta. Yana yana da babban m muhimmanci, kuma ta aikace-aikace damar sauri bayani da lissafai wata babbar domin.

Daya daga cikin kaddarorin da wannan Theorem ne kamar haka: da samfurin dukkan tushen da n-th mataki ne daidai da free members. Wannan dukiya ne sau da yawa amfani a warware lissafai na uku ko hudu mataki da nufin rage domin na polynomial. Idan polynomial n-th mataki yana da lamba Tushen, su za a iya sauƙi gano da wani sauki selection. Kuma m, ta hanyar aikata wani polynomial rabo a magana (x1-x), a polynomial (n-1) th digiri.

A karshen, za mu lura cewa Vieta Theorem ne daya daga cikin shahararrun theorems makaranta aljabara hanya. Kuma sunansa daukan wani cancanci wuri daga cikin sunayen mai girma lissafi.