Vieta kwakaita theorem no uye zvishoma nhoroondo

Vieta theorem no - vanzwisise kujairana chikoro anenge munhu wose. Asi kana iri "vanoshamwaridzana" chaizvoizvo? Shoma anosangana navo muupenyu hwezuva nezuva. Asi kwete vose vaya vari kubata masvomhu, dzimwe nguva kunzwisisa zvakadzama zvinoreva uye zvikuru kukosha theorem no ichi.

Vieta theorem no nyore zvikuru muitiro kugadzirisa akawandisa kwemasvomhu matambudziko, izvo pakupedzisira bikai pasi nezvokugadzirisa munhu quadratic mukana wokuti vanhu vanga :

ax2 + bx + C = 0, uko ≠ 0.

Ndiyo mureza chimiro quadratic mukana wokuti vanhu vanga. Kazhinji, yakadaro quadratic mukana wokuti vanhu vanga anga coefficients A, B, uye c, izvo zvinogona nyore nyore nokuda kupatsanura vapinde. Muchiitiko chino, tinosvika pana Zvichakadaro ari quadratic mukana wokuti vanhu vanga, inonzi akaderedza (kana coefficient pakati mukana wokuti vanhu vanga rokutanga akaenzana 1):

x2 + px + q = 0

It iri mhando equations uye zvakakunakira kushandisa theorem no kuti Vieta. The chikuru pfungwa theorem no ndechokuti zvinokosheswa yemidzi kv.uravneniya wakapiwa nomuromo hunogona kungoparara kutsunga nokuziva inokosha ukama Theorem:

• Verengai midzi akaenzana nokuwanda pakatarisana rechipiri coefficient (i.e., -p);
• chigadzirwa akaenzana rechitatu chinhu (kureva, q).

Kureva, x1 + x2 = -p, uye x1 * x2 = q.

Mutongo vakawanda matambudziko kuchikoro masvomhu ipfupi kuti nyore vachipiwa zvinove nyore kuwana nemutengo unyanzvi nhaka nomumukanwa kukarukureta. Hazvifaniri kukonzera zvinetso. Pane Ivan Kuchin theorem no kuti Vieta achibvumira yaivapo vachipiwa nhamba, inova midzi munhu quadratic mukana wokuti vanhu vanga, zviri nyore kuti kudzorera coefficients ayo uye unyore mureza chimiro.

Kugona kushandisa Vieta theorem no sechinhu zvikuru Kunoderedza kuti akarongeka uye mumuviri matambudziko muupenyu chesekondari. Kunyanya unyanzvi ichi rinokosha pakugadzirira vadzidzi kuti mukuru makirasi kuti bvunzo.

Achiziva kukosha yakadaro nyore uye inobudirira kwemasvomhu mudziyo, ndakanga ndisingagoni kubatsira kufunga munhu, kokutanga rinofanira kuzarurwa.

Fransua Viet - yakakurumbira musayendisiti French, uyo akatanga basa rake somunhu gweta. Asi, pachena, masvomhu aiva kudanwa kwake. Nepo roumambo basa sezvo gurukota, akava nomukurumbira, akakwanisa kuverenga intercepted coded mharidzo Mambo Spain kuNetherlands. Izvi zvakapa mambo French Henry III mukana kuziva zvose zvinovavarirwa vaimushora.

Zvishoma nezvishoma, sumo kune kwemasvomhu ruzivo, Fransua Viet akasvika pamhedziso kuti panofanira kuva pedyo kubatana pakati azvino panguva kuferefeta "algebraists" uye rakadzika nhaka yekare geometric. Nokufamba kwesainzi akasikirwa uye akagadzira pedyo zvinenge zvose zvokutanga nemasvomhu. Akatanga patange kushandiswa tsika chaiwo muna kwemasvomhu midziyo, pachena kusiyana pfungwa yokuti nhamba, uye kukosha ukama hwavo. Wyeth akaratidza kuti nokuita mabasa yokufananidzira chimiro, anogona kugadzirisa dambudziko iri vakawanda kudaro, nokuti zvinenge tsika dzose wainyatsotaura tsika.

kutsvakurudza yake nekugadzirisa equations kupfuura yechipiri, kwakaguma theorem no iyo yava kunzi Generalized Theorem pamusoro Vieta. It mukuru inoshanda kukosha, uye chikumbiro chacho chinoita kukurumidza kugadzirisa kuti equations ane yepamusoro kurongeka.

Mumwe zvivako ose theorem no uyu sezvinotevera: zvibereko zvose midzi yacho N-fung dhigirii akaenzana ayo vakasununguka nhengo. pfuma iyi rinowanzoshandiswa nekugadzirisa equations kuti dhigirii rechitatu kana kuti rechina nechinangwa kuderedza hurongwa polynomial. Kana polynomial N-fung dhigirii ane integer midzi, vanogona kuva nyore chinozivikanwa nyore vakasarudzwa. Uyezve, nokuita polynomial kupesana pamusoro okuti (x1-x), mumwe polynomial (n-1) fung dhigirii.

Pakupedzisira, tinoona kuti Vieta theorem no imwe yakakurumbira theorems chikoro nemasvomhu kosi. Uye zita rake anotora nzvimbo akafanira pakati mazita makuru mathematicians.