Lub hauv paus ntawm qhov equation - introductory ntaub ntawv

Nyob rau hauv algebra, muaj yog lub tswvyim ntawm ob hom ntawm koob pheej ntawm lawv - tus neeg thiab sib npaug. Yog leejtwg - cov no yog cov sib npaug zos, uas yog ua tau rau tag nrho cov qhov tseem ceeb ntawm cov ntawv uas ua rau lawv. Kab zauv - yog tseem sib npaug zos, tiam sis lawv yog ua tau tsuas yog rau cov qhov tseem ceeb ntawm lawv constituent cov tsiaj ntawv. Cov tsiaj ntawv nyob rau hauv lub tej yam kev mob ntawm qhov teeb meem no feem ntau yog tsis zoo tib. Qhov no txhais tau tias ib co ntawm lawv muaj peev xwm coj tej siv tau qhov tseem ceeb, hu ua coefficients (los yog tsis), thiab lwm tus neeg - lawv paub tias unknowns - lub ntsiab muaj nyob rau hauv cov tshuaj txheej txheem. Feem ntau, cov unknowns sawv cev rau cov tsiaj ntawv nyob rau hauv sib npaug tseeb nyob rau hauv lub Latin tsiaj ntawv (XYZ thiab lwm yam), los yog cov tib cov tsiaj ntawv tab sis nrog lub Performance index (x _1, x _2, etc.), raws li paub coefficients - thawj cov tsiaj ntawv ntawm tib cov niam ntawv.

Raws li cov xov tooj ntawm tsis paub hais tias paim kab zauv nrog ib tug, ob tug los yog ob peb unknowns. Yog li, tag nrho cov qhov tseem ceeb ntawm lub unknowns, uas daws kab zauv yuav ib tug yog leej twg, hu ua lub ntsiab ntawm qhov sib npaug. Cov kab zauv yuav suav hais tias daws nyob rau hauv cov kev tshwm sim hais tias tag nrho cov ntawm nws cov kev daws teeb meem muaj nyob los yog pov thawj hais tias nws tsis uas muaj tuaj. Ua hauj lwm "daws tau qhov equation" nyob rau hauv kev xyaum yog ib qho thiab txhais tau tias koj yuav tau mus nrhiav lub hauv paus ntawm kab zauv.

Lus Txhais: Cov hauv paus hniav ntawm cov kab zauv yog cov tseem ceeb ntawm cov unknowns ntawm lub kam rau ua, nyob rau hauv uas los mus daws cov kab zauv yuav ib tug yog leejtwg tiag.

algorithm daws sib npaug kiag li tag nrho cov tib yam, thiab cov ntsiab lus ntawm nws yog tias nrog kev pab los ntawm lej transformations no qhia ua rau ib tug yooj yim daim ntawv no.
Sib npaug uas muaj tib lub keeb kwm nyob rau algebra yog hu ua sib npaug.

Qhov yooj yim piv txwv 7x-49 = 0, lub hauv paus ntawm kab zauv x = 7;
x = 0 7, piv, lub hauv paus ntawm x = 7, yog li ntawd, yog sib npaug rau cov kab zauv. (Nyob rau hauv tshwj xeeb mob sib npaug rau cov kab zauv tej zaum yuav tsis muaj cov hauv paus hniav).

Yog hais tias lub hauv paus ntawm kab zauv tseem yog lub hauv paus ntawm lub lwm yam, ib tug yooj yim kab zauv muab los ntawm transformation ntawm lub qhov, lub tom kawg no yog hu ua ib tug txais ntawm txoj kev yav dhau los kab zauv.

Yog hais tias cov ob npaug ib tug yog lub qhov tsim nyog ntawm cov lwm yam, lawv pom tau hais tias yuav sib npaug. Tab sis lawv tau hu ua sib npaug. Qhov saum toj no piv txwv qhia txog qhov no.

Cov tshuaj ntawm txawm nyuaj sib npaug nyob rau hauv kev xyaum feem ntau ua rau cov teeb meem. Raws li ib tug tshwm sim, cov tshuaj yuav tau txais ib tug hauv paus ntawm qhov equation, ob lossis ntau dua, txawm tias ib tug infinite tooj - nws nyob ntawm lub hom sib npaug. Muaj cov neeg uas muaj tsis muaj keeb kwm, lawv hu ua intractable.

piv txwv:
1) 15 x 10 = -20; x = 2. Qhov no yog qhov hauv paus ntawm qhov equation.
2) 7x - y = 0. Cov kab zauv muaj infinite tus naj npawb ntawm cov hauv paus hniav, vim txhua nce mus nce los yuav ua tau ib tug countless tus naj npawb ntawm qhov tseem ceeb.
3) x = ² - 16. Tus xov tooj tsa mus rau lub thib ob degree, yeej ib txwm muab ib tug zoo tshwm sim, ces nws yog tsis yooj yim sua mus nrhiav lub hauv paus ntawm kab zauv. Qhov no yog ib tug ntawm cov unsolvable sib npaug hais saum toj no.

Correctness ntawm cov kev txiav txim siab yog muaj tseeb los ntawm hloov lub pom cov hauv paus hniav es tsis txhob ntawm cov tsiaj ntawv, thiab lub resulting tov piv txwv. Yog hais tias yog leejtwg yog respected, qhov kev txiav txim yog lawm.