Vieta lub theorem thiab ib tug me ntsis ntawm keeb kwm

Vieta theorem - ib lub tswvyim paub los ntawm lub tsev kawm ntawv yuav luag txhua leej txhua tus. Tab sis seb nws yog "paub" tiag tiag? Ob peb encounters lawv nyob rau hauv lub neej txhua hnub. Tab sis tsis yog txhua txhua cov neeg uas yog kev soj ntsuam txog nrog kev kawm txog zauv, tej zaum tag nrho to taub sib sib zog nqus ntsiab lus thiab kuj zoo kawg tseem ceeb ntawm no theorem.

Vieta theorem heev simplifies tus txheej txheem kev daws ib tug lossis loj tus naj npawb ntawm zauv teeb meem, uas thaum kawg rhaub down rau kev daws ib quadratic equation :

ax2 + bx + c = 0, qhov twg ib tug ≠ 0.

Qhov no yog tus qauv hauv daim ntawv ntawm cov quadratic equation. Nyob rau hauv feem ntau tus neeg mob, xws li ib tug quadratic equation tau coefficients ib tug, b, thiab c, uas yuav tsum tau nkag yooj yim zog los mus faib lawv mus rau hauv ib tug. Nyob rau hauv cov ntaub ntawv no, peb txog ntawm tus phem ntawm lub quadratic equation, hu txo (thaum thawj coefficient ntawm kab zauv yog sib npaug zos rau 1):

x2 + px + q = 0

Nws yog rau no hom ntawm cov equations thiab yooj yim rau siv cov theorem ntawm Vieta. Lub ntsiab kev txiav txim zoo theorem yog tias qhov tseem ceeb ntawm cov keeb kwm kv.uravneniya muab lus yuav muab tau yooj yim txiav txim los ntawm kev paub txog qhov yooj yim kev sib raug zoo ntawm Theorem:

• sum ntawm cov keeb kwm yog sib npaug zos rau cov xov tooj ntawm opposite thib ob coefficient (i.e., -p);
• Cov khoom no yog sib npaug zos rau peb tau (ie, q).

Namely, x1 + x2 = -p, thiab x1 * x2 = q.

Qhov kev txiav txim ntawm feem ntau ntawm cov teeb meem nyob rau hauv lub tsev kawm ntawv kev kawm txog zauv yog txo mus rau ib tug yooj yim khub ntawm cov zauv uas yog ib qho yooj yim mus nrhiav tau rau ntawm yam tsawg kawg nkaus txawj muaj qhov ncauj muab xam. Thiab nws yuav tsum tsis txhob ua tej yam teeb meem. Muaj yog ib qho kev rov qab theorem ntawm Vieta tso cai rau uas twb muaj lawm khub ntawm cov zauv, uas yog cov hauv paus hniav ntawm ib tug quadratic equation, nws yog ib qho yooj yim mus rau restore nws coefficients thiab sau nyob rau hauv daim ntawv.

Muaj peev xwm siv cov Vieta theorem li ib lub cuab tam loj alleviates cov zauv thiab lub cev muaj teeb meem nyob rau hauv lub chav kawm ntawm high school. Tshwj xeeb tshaj yog no kev txawj yog indispensable nyob rau hauv kev npaj cov tub ntxhais kawm ntawm senior cov chav kawm rau cov tub ntxhais.

Realizing qhov tseem ceeb ntawm xws li ib tug yooj yooj yim thiab zoo xyuam xim cuab tam, kuv yuav pab tsis tau xav seb ib tug txiv neej, cov thawj lub sij hawm nws yog qhib.

Fransua Viet - tus naas ej Fabkis tus paub txog, uas pib nws cov hauj lwm raws li ib tug kws lij choj. Tab sis, obviously, lej yog nws txoj hauj lwm. Thaum muaj koob muaj npe ua ib tug kws pab tswv yim, nws ua nto moo, nws muaj peev xwm nyeem ntawv rau kev cuam tshuam coded lus ntawm tus huab tais ntawm Spain mus rau lub Netherlands. Qhov no muab lub Fabkis huab tais Henry III lub sij hawm los mus paub txog tag nrho cov intentions ntawm nws tw.

Maj mam, ib tug taw qhia rau zauv paub, Fransua Viet tuaj mus rau lub xaus hais tias muaj yuav tsum yog ib tug nyob ze kev twb kev txuas ntawm qhov tseeb thaum lub sij hawm tshawb nrhiav "algebraists" thiab ib tug sib sib zog nqus cuab yeej cuab tam ntawm ancient geometric. Nyob rau hauv lub chav kawm ntawm kev tshawb fawb nws tau tsim thiab formulated los ntawm yuav luag tag nrho cov elementary algebra. Nws ua ntej nkag tau rau kev siv ntawm literal qhov tseem ceeb nyob rau hauv cov zauv apparatus, ib tug ntshiab qho uas txawv ntawm lub tswvyim ntawm ib tug xov tooj, thiab tus nqi ntawm lawv cov kev sib raug zoo. Wyeth pom tias los ntawm kev ua hauj lwm nyob rau hauv ib lub cim daim ntawv no, muaj peev xwm daws tau qhov teeb meem nyob rau hauv cov kev cov ntaub ntawv, rau yuav luag tag nrho cov tseem ceeb ntawm cov kev cai tswjhwm qhov tseem ceeb.

Nws kev tshawb fawb daws sib npaug ntau tshaj lub thib ob, tau nyob rau hauv ib tug theorem uas yog tam sim no lub npe hu ua lub Generalized Theorem ntawm Vieta. Nws muaj ib tug zoo tswv yim tseem ceeb, thiab nws daim ntawv thov yuav pab ib tug ceev cov tshuaj rau qhov sib npaug ntawm ib tug ntau dua kev txiav txim.

Ib tug ntawm cov yam ntxwv ntawm no theorem yog raws li nram no: cov khoom ntawm tag nrho cov hauv paus hniav ntawm tus n-th degree yog sib npaug zos rau nws free neeg. Qhov no tej khoom vaj tse yog feem ntau siv nyob rau hauv kev daws sib npaug ntawm peb los yog plaub degree nrog rau cov aim ntawm kev txo qhov kev txiav txim ntawm lub polynomial. Yog hais tias lub polynomial n-th degree muaj integer keeb kwm, lawv muaj peev xwm muab tau yooj yim qhia los ntawm ib tug yooj yim xaiv. Thiab ntxiv, los ntawm kev ua ib tug polynomial division rau cov kev qhia (x1-x), ib tug polynomial (n-1) th degree.

Nyob rau hauv lub kawg, peb nco ntsoov tias cov Vieta theorem yog ib lub npe nrov tshaj theorems tsev kawm ntawv algebra kawg. Thiab nws lub npe yuav siv sij hawm ib tug tsim nyog qhov chaw ntawm cov npe ntawm cov poj mathematicians.