Tauwehe o Vieta me te moka o te hītori

Vieta ture tauwehe - te ariā maheni i te kura tata katoa. Otiia ahakoa he reira "maheni" tino? farerei atu torutoru ratou i roto i te ora ia rā. Otiia e kore e te hunga e e pā ana ki te pāngarau katoa, i ētahi wā tino matau te auraa hohonu me te faufaa rahi o tenei ture tauwehe.

Vieta ture tauwehe nui ohie te tukanga o te whakaoti i te tau nui o ngā raruraru pāngarau, e te mutunga kohuatia iho ki whakaoti i te whārite pūrua :

ax2 + bx + c = 0, te wahi i te ≠ 0.

Ko te ahua paerewa o te whārite pūrua tenei. I roto i te nuinga o te wā, kua tau whakarea i te taua whārite pūrua he, b, me c, e taea te ngāwari māmā e wehewehe ratou ki te. I roto i tenei take, tae tatou i te tau toharite o te whārite pūrua, huaina te heke (ina he rite te whakarea tuatahi o te whārite ki te 1):

x2 + px + q = 0

Ko reira hoki tenei momo o whārite, me te watea ki te whakamahi i te ture tauwehe o Vieta. Ko te ture tauwehe tikanga matua ko e te uara o te kv.uravneniya homai waha pakiaka taea te ngāwari whakaritea e mohio ki te pā ana taketake o te Ariā:

• Ko rite ki te maha o te whakarea tuarua ritenga (i.e., -p) moni o nga pakiaka;
• He rite ki te toru o nga take (arā, q) hua.

Ara, x1 + x2 = -p, me x1 * x2 = q.

iti te whakatau o te nuinga o ngā raruraru i roto i te pāngarau kura te ki te rua ohie o ngā tau e he ngāwari ki te kitea i ngā pūkenga iti kainga o tātaitanga ā-waha. A e kore e meinga te reira tetahi raruraru. He he he ture tauwehe kōaro o Vieta taea hoki rua tīariari o tau, e ko te pakiaka o te whārite pūrua, e mea ohie ki te whakahokia ona tau whakarea, me te tuhituhi i roto i te puka paerewa.

Te āhei ki te whakamahi i te ture tauwehe Vieta rite te taputapu nuinga E faaiti te raruraru pāngarau, me te tinana i roto i te akoranga o te kura nui. Rawa tenei pūkenga he mahuinga i te whakarite ngā ākonga o ngā akomanga matua mo te whakamātautau.

Te ite i te faufaa o te taua taputapu pāngarau ohie, me te whai hua, e kore i taea e ahau te āwhina whakaaro o te tangata, te wā tuatahi kua whakatuwheratia reira.

Fransua Viet - te pūtaiao French rongonui, e timata tona mahi rite te rōia. Ko, mea papû e, ko te pāngarau tona piiraa. Ahakoa te mahi kingi rite te kaiwhakatakoto whakaaro, ka ia rongonui, i taea e ki te pānui i te karere ā haukotia o te Kingi o Spain ki te Netherlands ia. hoatu tenei te kingi French Henry III te whai wāhi ki te mohio e pā ana ki nga whakaaro katoa o tona hoariri.

Āta, he whakataki ki te matauranga pāngarau, ka haere Fransua Viet ki te mutunga e reira me waiho he hononga tata i waenganui i te hou i te wa tūhuratanga "algebraists" me te kainga tupu hohonu o āhuahanga tahito. I roto i te akoranga o te rangahau pūtaiao i hangaia ai, ka whakatakoto e tata katoa taurangi pūmotu. Ia te tuatahi whakaurua te whakamahi o ngā uara mau i roto i te taputapu pāngarau, he rereketanga mārama i waenganui i te ariā o te tau, me te uara o to ratou hononga. whakakitea Wyeth e na roto i te raveraa i ngā mahi i roto i te puka tohu, ka taea e te whakaoti i te raruraru i roto i te take whānui, hoki tata uara katoa o te uara i tohua.

Tona rangahau mō te whakaoti whārite, nui atu i te tuarua, hua i roto i te ture tauwehe e te mohiotia inaianei rite te whānui Ariā o Vieta. He he mahu'inga nui mahi, me tona tono e āhei te otinga tere ki te whārite o te tikanga teitei.

Ko tētahi o nga āhuatanga o tenei ture tauwehe ko e whai ake: ko te hua o katoa nga pakiaka o te tohu n-th he rite ki ona mema o free. Kei te maha whakamahia tēnei taonga i roto i te whakaoti whārite o te toru ranei te wha tohu ki te whāinga o te whakaiti i te tikanga o te pūrau. Ki te he pakiaka tōpū te tohu n-th pūrau, e taea te ngāwari tāutuhia ratou e te kōwhiringa ohie. A atu, na roto i te raveraa i te wehenga pūrau i runga i te whakapuaki (x1-x), he pūrau (n-1) th tohu.

I roto i te mutunga, i kite mātou i te ture tauwehe Vieta ko tetahi o te akoranga taurangi theorems kura tino rongonui. A e tona ingoa he wahi tika i roto i te ingoa o te pāngarau nui.