Kev daws qhov sib npaug hauv lej muaj qhov tshwj xeeb. Cov txheej txheem no yog ua ntej los ntawm ntau teev ntawm kev kawm txoj kev xav, thaum lub sij hawm cov tub ntxhais kawm kawm yuav ua li cas los daws qhov sib npaug, txiav txim siab lawv daim ntawv thiab coj cov txuj ci mus rau tag nrho automatism. Txawm li cas los xij, kev tshawb nrhiav cov hauv paus hniav tsis yog ib txwm ua rau kev nkag siab, vim lawv tsuas yog tsis muaj nyob. Muaj txoj hauv kev tshwj xeeb los nrhiav cov hauv paus hniav. Hauv tsab xov xwm no, peb yuav txheeb xyuas cov haujlwm tseem ceeb, lawv cov peev txheej, nrog rau cov xwm txheej uas lawv cov cag tsis tuaj.
Kev sib npaug twg tsis muaj hauv paus?
Ib qho kev sib npaug tsis muaj hauv paus yog tias tsis muaj qhov sib cav tiag tiag x uas qhov sib npaug yog qhov tseeb. Rau cov tsis yog tus kws tshaj lij, cov qauv no, zoo li feem ntau ntawm kev ua lej thiab cov qauv, zoo li tsis meej pem thiab paub daws teeb, tab sis qhov no yog nyob rau hauv txoj kev xav. Hauv kev xyaum, txhua yam ua tau yooj yim heev. Piv txwv li: qhov sib npaug 0x=-53 tsis muaj kev daws teeb meem, vim tsis muaj tus lej x, cov khoom uas muaj xoom yuav muab lwm yam uas tsis yog xoom.
Tam sim no peb yuav saib cov hom kev sib npaug tshaj plaws.
1. linear equation
Ib qho kev sib npaug hu ua linear yog tias nws txoj cai thiab sab laug yog sawv cev raws li cov haujlwm ua haujlwm: ax + b=cx + d lossis hauv daim ntawv dav dav kx + b=0. Qhov twg a, b, c, d paub tus lej, thiab x yog qhov tsis paub ntau. Qhov kev sib npaug twg tsis muaj hauv paus? Piv txwv ntawm cov kab zauv sib npaug muaj nyob rau hauv cov duab hauv qab no.
Yeej, cov kab zauv sib npaug yog daws los ntawm kev txav tus lej mus rau ib feem thiab cov ntsiab lus ntawm x mus rau lwm qhov. Nws hloov tawm qhov sib npaug ntawm daim ntawv mx \u003d n, qhov twg m thiab n yog tus lej, thiab x yog qhov tsis paub. Txhawm rau nrhiav x, nws txaus los faib ob qhov chaw los ntawm m. Ces x=n/m. Yeej, cov kab sib npaug tsuas muaj ib lub hauv paus xwb, tab sis muaj cov xwm txheej thaum muaj ntau cov hauv paus hniav los yog tsis muaj dab tsi. Nrog m=0 thiab n=0, qhov sib npaug yuav siv daim ntawv 0x=0. Txhua tus lej yuav yog qhov kev daws teeb meem rau qhov sib npaug.
Tab sis dab tsi sib npaug tsis muaj hauv paus?
Thaum m=0 thiab n=0, qhov sib npaug tsis muaj hauv paus los ntawm cov lej tiag. 0x=-1; 0x=200 - cov kab zauv no tsis muaj hauv paus.
2. Quadratic equation
A quadratic equation is an equation of the form ax2 + bx + c=0 for a=0. Feem ntau txoj hauv kev los daws qhov kev sib npaug plaub npaug yog daws nws los ntawm kev ntxub ntxaug. Cov mis rau kev nrhiav qhov tsis sib haum xeeb ntawm ib qho kev sib npaug sib npaug: D=b2 - 4ac. Ces muaj ob lub hauv paus x1, 2=(-b ± √D) / 2a.
Thaum D > 0 qhov sib npaug muaj ob lub hauv paus, thaum D=0 - ib lub hauv paus. Tab sis dab tsi quadratic equation tsis muaj hauv paus?Txoj hauv kev yooj yim tshaj plaws los saib xyuas cov hauv paus hauv paus ntawm kev sib npaug plaub npaug yog nyob ntawm daim duab ntawm ib qho kev ua haujlwm, uas yog parabola. Ntawm > 0 cov ceg raug coj mus rau sab saud, ntawm < 0 cov ceg raug txo qis. Yog tias qhov kev ntxub ntxaug tsis zoo, qhov sib npaug plaub npaug tsis muaj cov hauv paus hauv cov lej tiag.
Koj tuaj yeem pom qhov pom ntawm cov hauv paus hniav yam tsis suav cov neeg sib cais. Txhawm rau ua qhov no, koj yuav tsum nrhiav qhov saum toj kawg nkaus ntawm parabola thiab txiav txim siab nyob rau hauv qhov kev taw qhia ntawm cov ceg ntoo. Koj tuaj yeem txiav txim siab x-coordinate ntawm ib qho vertex siv tus qauv: x0 =-b / 2a. Hauv qhov no, y-coordinate ntawm lub vertex yog pom los ntawm tsuas yog hloov qhov x0 tus nqi rau hauv qhov sib npaug qub.
Kev sib npaug plaub x2 – 8x + 72=0 tsis muaj cov hauv paus hniav vim nws muaj qhov tsis zoo sib cais D=(–8)2 - 4172=-224. Qhov no txhais tau hais tias lub parabola tsis kov x-axis thiab qhov ua haujlwm yeej tsis siv tus nqi 0, yog li qhov sib npaug tsis muaj cov hauv paus tiag tiag.
3. Trigonometric equations
Trigonometric functions raug txiav txim siab ntawm lub voj voog trigonometric, tab sis kuj tuaj yeem sawv cev hauv Cartesian kev tswj hwm. Hauv tsab xov xwm no, peb yuav saib ob txoj haujlwm trigonometric yooj yim thiab lawv qhov sib npaug: sinx thiab cosx. Txij li cov haujlwm no tsim lub voj voog trigonometric nrog lub vojvoog 1, |sinx| and |cosx| tsis tuaj yeem ntau dua 1. Yog li qhov sib npaug sinx tsis muaj cov hauv paus hniav? Xav txog cov duab ntawm sinx muaj nuj nqi uas qhia hauv daim duabhauv qab no.
Peb pom tias txoj haujlwm sib luag thiab muaj lub sijhawm rov ua dua ntawm 2pi. Raws li qhov no, peb tuaj yeem hais tias tus nqi siab tshaj ntawm qhov kev ua haujlwm no tuaj yeem yog 1, thiab qhov tsawg kawg nkaus -1. Piv txwv li, cov lus qhia cosx=5 yuav tsis muaj cov hauv paus hniav, vim nws cov modulo ntau dua ib.
Qhov no yog qhov piv txwv yooj yim ntawm kev sib npaug trigonometric. Qhov tseeb, lawv cov kev daws teeb meem tuaj yeem siv ntau nplooj ntawv, thaum kawg ntawm qhov koj paub tias koj siv cov mis tsis raug thiab koj yuav tsum pib dua. Qee lub sij hawm, txawm tias qhov kev tshawb pom tseeb ntawm cov hauv paus hniav, koj tuaj yeem hnov qab coj mus rau hauv tus account cov kev txwv ntawm ODZ, uas yog vim li cas lub hauv paus ntxiv los yog ncua sij hawm tshwm sim hauv cov lus teb, thiab tag nrho cov lus teb hloov mus rau qhov yuam kev. Yog li ntawd, nruj me ntsis ua raws li tag nrho cov kev txwv, vim hais tias tsis yog tag nrho cov hauv paus hniav haum rau lub Scope ntawm txoj hauj lwm.
4. Systems of Equations
Ib qho kev sib npaug yog ib qho kev sib npaug ua ke nrog curly lossis square brackets. Curly braces qhia txog kev sib koom ua tiav ntawm txhua qhov sib npaug. Ntawd yog, yog tias tsawg kawg ib qho ntawm qhov sib npaug tsis muaj cov hauv paus hniav lossis tsis sib haum xeeb, tag nrho cov kab ke tsis muaj kev daws teeb meem. Square brackets qhia lo lus "los yog". Qhov no txhais tau hais tias yog tsawg kawg ib qho kev sib npaug ntawm qhov system muaj kev daws teeb meem, ces tag nrho cov kab ke muaj kev daws teeb meem.
Cov lus teb ntawm lub kaw lus nrog cov kab lus square yog tag nrho ntawm tag nrho cov hauv paus hniav ntawm tus kheej sib npaug. Thiab cov kab ke nrog curly braces tsuas muaj cov hauv paus hniav xwb. Cov txheej txheem ntawm kev sib npaug tuaj yeem suav nrog ntau yam kev ua haujlwm, yog li qhov nyuaj no tsis yogtso cai rau koj qhia tam sim ntawd qhov sib npaug tsis muaj hauv paus.
Kev qhia dav dav thiab cov lus qhia txhawm rau nrhiav cov hauv paus ntawm kab zauv
Hauv cov ntawv teeb meem thiab phau ntawv kawm muaj ntau hom kev sib npaug: cov uas muaj hauv paus, thiab cov uas tsis muaj lawv. Ua ntej tshaj plaws, yog tias koj nrhiav tsis tau cov hauv paus hniav, tsis txhob xav tias lawv tsis muaj nyob rau hauv tag nrho. Tej zaum koj yuav tau ua yuam kev nyob qhov twg, ces cia li muab ob npaug rau-xyuas koj cov tshuaj.
Peb tau them cov kev sib npaug yooj yim tshaj plaws thiab lawv hom. Tam sim no koj tuaj yeem qhia qhov sib npaug uas tsis muaj cov hauv paus hniav. Feem ntau, qhov no tsis yog qhov nyuaj ua. Txhawm rau kom ua tiav qhov kev daws teeb meem sib npaug, tsuas yog yuav tsum tau ua tib zoo mloog thiab mloog zoo. Xyaum ntau dua, nws yuav pab koj taug qab cov khoom zoo dua thiab sai dua.
Yog li, qhov sib npaug tsis muaj hauv paus yog:
- hauv kab zauv mx=n tus nqi m=0 thiab n=0;
- nyob rau hauv ib qho kev sib npaug plaub yog tias qhov kev ntxub ntxaug tsawg dua xoom;
- hauv qhov sib npaug trigonometric ntawm daim ntawv cosx=m / sinx=n, yog |m| > 0, |n| > 0;
- nyob rau hauv ib qho kev sib npaug nrog curly brackets yog tias tsawg kawg ib qho kev sib npaug tsis muaj cov hauv paus, thiab nrog cov square brackets yog tias txhua qhov sib npaug tsis muaj cov hauv paus.
