Kev paub txog algebra yog qhov tseem ceeb rau kev txuas ntxiv mus yuav luag txhua hom lej, txawm hais tias nyob hauv tsev kawm theem qis lossis theem siab. Txhua qib lej muaj lub hauv paus, yog li txhua qib lej yog qhov tseem ceeb heev. Txawm li cas los xij, txawm tias cov txuj ci algebraic yooj yim tshaj plaws tuaj yeem nyuaj rau cov pib nkag siab thawj zaug uas lawv ntsib lawv. Yog tias koj muaj teeb meem nrog cov ncauj lus yooj yim algebra, tsis txhob txhawj xeeb - nrog kev piav qhia me ntsis, ob peb yam piv txwv yooj yim, thiab ob peb lub tswv yim txhawm rau txhim kho koj cov txuj ci, koj yuav sai sai no daws teeb meem algebra zoo li tus kws tshaj lij.
Kauj ruam
Ntu 1 ntawm 5: Kawm Txoj Cai Tseem Ceeb ntawm Algebra
Kauj Ruam 1. Txheeb xyuas koj cov lej lej yooj yim
Txhawm rau pib kawm lej, koj yuav tsum paub cov txuj ci ua lej xws li ntxiv, rho tawm, sib npaug, thiab faib ua ke. Qhov lej/tsev kawm ntawv theem pib no tseem ceeb heev ua ntej koj pib kawm algebra. Yog tias koj tsis paub cov txuj ci no, nws yuav nyuaj rau ua kom tiav cov ntsiab lus nyuaj uas qhia hauv algebra. Yog tias koj xav tau kev kho dua tshiab rau cov haujlwm no, sim peb kab lus ntawm kev txawj ua lej yooj yim.
Koj tsis tas yuav ua tau zoo ntawm kev ua cov haujlwm yooj yim no hauv koj lub taub hau los ua teeb meem algebra. Ntau chav kawm algebra tso cai rau koj siv lub laij lej kom txuag sijhawm thaum ua cov haujlwm yooj yim no. Txawm li cas los xij, koj yuav tsum paub tsawg kawg yuav ua li cas ua cov haujlwm no yam tsis muaj lub laij lej thaum koj tsis raug tso cai siv lub laij lej
Kauj Ruam 2. Paub qhov kev txiav txim ntawm kev ua haujlwm
Ib qho uas nyuaj tshaj plaws txog kev daws cov lej sib npaug ua tus pib yog paub qhov kev txiav txim uas lawv pib. Hmoov zoo, muaj qee qhov kev txiav txim los daws cov teeb meem no: ua ntej, ua ib qho kev ua lej nyob rau hauv kab lus, tom qab ntawd ua cov lus piav qhia, tom qab ntawd sib npaug, tom qab ntawd faib, tom qab ntawd ntxiv, thiab thaum kawg rho tawm. Ib qho txiaj ntsig zoo ntawm kev nco qab qhov kev txiav txim ntawm cov haujlwm no yog cov ntawv luv KPKBJK. Kawm paub yuav siv qhov kev txiav txim ntawm kev ua haujlwm ntawm no. Yuav kom xaus, qhov kev txiav txim ntawm kev ua haujlwm yog:
- Kswb
- Pnqa/nthuav tawm
- Klwm
- Bdua
- Jumlah ua
- Kcws
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Kev txiav txim ntawm kev ua haujlwm yog ib qho tseem ceeb hauv algebra vim tias ua cov haujlwm hauv ib qho teeb meem algebra hauv qhov kev txiav txim tsis raug tuaj yeem qee zaum cuam tshuam rau cov lus teb. Piv txwv, yog tias peb ua lej lej 8 + 2 × 5, yog tias peb ntxiv 2 thiab 8 ua ntej, peb tau txais 10 × 5 = 50, tab sis yog tias peb faib 2 thiab 5 ua ntej, peb tau txais 8 + 10 =
Kauj ruam 18.. Tsuas yog lo lus teb thib ob yog qhov raug.
Kauj Ruam 3. Paub siv tus lej tsis zoo
Hauv algebra, kev siv tus lej tsis zoo yog qhov ntau heev. Yog li nws yog lub tswv yim zoo los tshuaj xyuas yuav ntxiv, rho tawm, sib npaug, thiab faib cov lej tsis zoo ua ntej koj pib kawm lej. Nov yog qee qhov lej tsis zoo hauv qab kom nco qab - rau cov ntaub ntawv ntau ntxiv, txheeb xyuas peb cov ntawv ntawm kev ntxiv thiab rho tawm cov lej tsis zoo thiab faib thiab muab cov lej tsis zoo.
- Ntawm tus lej kab, qhov tsis zoo ntawm tus lej yog tib qhov deb ntawm xoom raws li tus lej zoo yog los ntawm xoom, tab sis nyob hauv qhov kev coj rov qab.
- Ntxiv ob tus lej tsis zoo ua rau tus lej tsis zoo dua (hauv lwm lo lus, tus lej yuav loj dua, tab sis vim tus lej tsis zoo, tus nqi yuav me dua)
- Ob lub cim tsis zoo thim ib leeg tawm - rho tus lej tsis zoo yog tib yam li ntxiv tus lej zoo
- Kev sib npaug lossis faib ob tus lej tsis zoo muab cov lus teb zoo.
- Kev sib npaug lossis faib tus lej zoo thiab tus lej tsis zoo muab cov lus teb tsis zoo.
Kauj Ruam 4. Paub tsim cov lus nug ntev
Thaum cov teeb meem algebra yooj yim tuaj yeem daws tau yooj yim, teeb meem nyuaj tuaj yeem xav tau ntau qib. Txhawm rau zam kev ua yuam kev, khaws koj txoj haujlwm ua haujlwm los ntawm kev pib kab tshiab txhua lub sijhawm koj nqis tes ua kom tiav koj cov teeb meem. Yog tias koj tab tom ua haujlwm nrog ob tog sib npaug, sim sau txhua qhov sib npaug ntawm cov cim ("=") hauv qab lwm qhov cim sib npaug. Txoj kev no, yog koj ua yuam kev nyob qhov twg, nws yuav yooj yim dua nrhiav thiab kho nws.
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Piv txwv, los daws qhov sib npaug 9/3 - 5 + 3 × 4, peb yuav tuaj yeem tsim qauv peb cov teeb meem zoo li no:
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- 9/3 - 5 + 3 × 4
- 9/3 - 5 + 12
- 3 - 5 + 12
- 3 + 7
- Kauj ruam 10.
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Ntu 2 ntawm 5: Nkag Siab Txog Qhov Hloov Pauv
Kauj Ruam 1. Nrhiav cov cim uas tsis yog tus lej
Hauv algebra, koj yuav pib pom cov tsiaj ntawv thiab cov cim tshwm hauv koj cov teeb meem lej, tsis yog tus lej. Cov tsiaj ntawv thiab cov cim no hu ua qhov hloov pauv. Variables tsis ສັບ ສົນ li lawv yuav zoo li pom thawj zaug - lawv tsuas yog ib txoj hauv kev los sau cov lej uas tsis paub qhov tseem ceeb. Hauv qab no tsuas yog qee qhov piv txwv ntawm cov lej hauv algebra:
- Cov ntawv zoo li x, y, z, a, b, thiab c
- Cov ntawv Greek zoo li theta lossis
- Nco ntsoov tias tsis yog txhua lub cim tsis paub qhov txawv. Piv txwv li, pi, lossis, ib txwm sib npaug li 3.1459.
Kauj Ruam 2. Xav txog qhov hloov pauv ua tus lej "tsis paub"
Raws li tau hais los saum toj no, cov kev hloov pauv tsuas yog cov lej uas tsis paub qhov tseem ceeb. Feem ntau, koj lub hom phiaj hauv teeb meem algebra yog txhawm rau nrhiav qhov txiaj ntsig ntawm qhov sib txawv - xav txog qhov sib txawv raws li "tus lej tsis paub" koj tab tom sim nrhiav.
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Piv txwv, hauv kab zauv 2x + 3 = 11, x yog peb qhov sib txawv. Qhov no txhais tau tias muaj ntau qhov txiaj ntsig uas coj mus rau qhov chaw x ua rau sab laug ntawm qhov sib npaug sib npaug 11. Txij li 2 × 4 + 3 = 11, hauv qhov no, x =
Kauj ruam 4..
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Ib txoj hauv kev yooj yim los pib nkag siab qhov sib txawv yog hloov lawv nrog cov lus nug hauv cov teeb meem algebra. Piv txwv li, peb tuaj yeem sau qhov sib npaug 2 + 3 + x = 9 ua 2 + 3 +?
= 9. Qhov no ua rau peb nkag siab yooj yim txog yam peb tab tom sim ua - peb tsuas yog yuav tsum nrhiav tus nqi uas yuav tsum tau ntxiv rau 2 + 3 = 5 kom tau txais 9. Ib zaug ntxiv, tau kawg cov lus teb yog
Kauj ruam 4..
Kauj Ruam 3. Yog tias muaj qhov sib txawv tshwm sim ntau dua ib zaug, hloov pauv qhov sib txawv
Koj yuav ua dab tsi yog tias tib qhov sib txawv tshwm ntau dua ib zaug hauv ib qho zauv? Thaum qhov xwm txheej no yuav zoo li nyuaj rau daws, koj tuaj yeem kho cov kev hloov pauv zoo ib yam li koj tus lej ib txwm - hauv lwm lo lus, koj tuaj yeem ntxiv lawv, rho tawm lawv, thiab ntxiv rau, tsuav yog koj tsuas yog sib xyaw ua ke zoo ib yam. Hauv lwm lo lus, x + x = 2x, tab sis x + y tsis sib npaug rau 2xy.
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Piv txwv, cia saib ntawm qhov sib npaug 2x + 1x = 9. Hauv qhov teeb meem no, peb tuaj yeem ntxiv 2x thiab 1x kom tau 3x = 9. Txij li 3 x 3 = 9, peb paub tias x =
Kauj ruam 3..
- Nco tseg dua tias koj tsuas tuaj yeem ntxiv qhov sib txawv ua ke. Hauv qhov sib npaug 2x + 1y = 9, peb tsis tuaj yeem ua ke 2x thiab 1y vim tias lawv txawv txav sib txawv.
- Qhov no kuj siv tau thaum ib qho kev hloov pauv muaj qhov sib txawv piav qhia ntau dua li lwm qhov sib txawv. Piv txwv li, hauv kab zauv 2x + 3x2 = 10, peb tsis tuaj yeem ua ke 2x thiab 3x2 vim qhov sib txawv x muaj qhov sib txawv nthuav tawm. Saib yuav ua li cas ntxiv cov ntsiab lus nthuav qhia ntxiv.
Ntu 3 ntawm 5: Kawm Yuav Ua Li Cas Thiaj Li Muab Qhov Sib Txawv Los Ntawm "Tsis Pom Zoo"
Kauj Ruam 1. Sim cais cov sib txawv hauv cov lej sib npaug algebraic
Kev daws qhov sib npaug hauv algebra feem ntau txhais tau tias nrhiav tus nqi ntawm qhov sib txawv. Algebraic equations feem ntau suav nrog cov lej thiab/lossis qhov sib txawv ntawm ob sab, zoo li no: x + 2 = 9 × 4. Txhawm rau nrhiav tus nqi ntawm qhov sib txawv, koj yuav tsum cais qhov sib txawv ntawm ib sab ntawm qhov sib npaug kos npe. Txawm li cas los xij ntawm lwm sab ntawm qhov sib npaug kos npe yog koj cov lus teb.
Hauv qhov piv txwv (x + 2 = 9 × 4), txhawm rau cais x ntawm sab laug ntawm qhov sib npaug, peb yuav tsum tshem tawm " + 2". Txhawm rau ua qhov no, peb tsuas yog yuav tsum rho 2 los ntawm sab ntawd, tso peb nrog x = 9 × 4. Txawm li cas los xij, txhawm rau ua kom ob sab ntawm qhov sib npaug sib npaug, peb kuj yuav tsum rho 2 los ntawm lwm sab. Qhov no tawm peb nrog x = 9 × 4 - 2. Ua raws qhov kev txiav txim ntawm kev ua haujlwm, peb ua ntej sib npaug, tom qab ntawd rho tawm, muab peb cov lus teb x = = 36 - 2 = 34.
Kauj Ruam 2. Tshem tawm qhov sib ntxiv los ntawm kev rho tawm (thiab rov ua dua)
Raws li peb nyuam qhuav pom saum toj no, cais x ntawm ib sab ntawm qhov sib npaug kos npe feem ntau txhais tau tias tshem tawm cov lej nyob ib sab ntawm nws. Txhawm rau ua qhov no, peb ua haujlwm "thim rov qab" ntawm ob sab ntawm qhov sib npaug. Piv txwv, hauv kab zauv x + 3 = 0, txij li peb pom " + 3" tom qab peb x, peb yuav tso "-3" ntawm ob sab. "+3" thiab "-3", tawm x nyob ib leeg thiab "-3" ntawm lwm sab ntawm qhov sib npaug kos npe, zoo li no: x = -3.
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Feem ntau, ntxiv thiab rho tawm zoo li "thim rov qab" - suav ib qho haujlwm kom pov tseg lwm qhov. Saib hauv qab no:
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- Ntxiv rau, rho tawm. Piv txwv: x + 9 = 3 → x = 3 - 9
- Rau kev rho tawm, ntxiv. Piv txwv: x - 4 = 20 → x = 20 + 4
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Kauj Ruam 3. Tshem tawm qhov sib npaug los ntawm kev faib (thiab rov ua dua)
Kev sib npaug thiab faib ua haujlwm nyuaj me ntsis dua li kev ntxiv thiab rho tawm, tab sis cov kev suav no muaj tib yam "thim rov qab" kev sib raug zoo. Yog tias koj pom "× 3" ntawm ib sab, koj yuav tsis pom zoo nws los ntawm faib ob sab los ntawm 3, thiab ntxiv rau.
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Nrog kev sib npaug thiab faib, koj yuav tsum ua qhov rov qab ua haujlwm rau txhua tus lej uas nyob ntawm lwm sab ntawm qhov sib npaug kos npe, txawm tias sab ntawd muaj ntau dua ib tus lej. Saib hauv qab no:
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- Rau kev sib npaug, faib. Piv txwv: 6x = 14 + 2 → x = (14 + 2) /6
- Rau kev faib, sib npaug. Piv txwv: x/5 = 25 → x = 25 × 5
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Kauj Ruam 4. Tshem tawm qhov nthuav tawm los ntawm kev nrhiav lub hauv paus (thiab rov ua dua)
Cov neeg nthuav tawm yog cov ncauj lus zoo ua ntej ua lej algebra - yog tias koj tsis paub yuav ua li cas, ua tibzoo saib ntawm peb kab lus nthuav dav nthuav dav rau cov ntaub ntawv ntau ntxiv. "Thim rov qab" ntawm cov lus piav qhia yog lub hauv paus uas muaj tus lej zoo ib yam li cov lus piav qhia. Piv txwv li, qhov sib txawv ntawm tus exponent 2 yog lub hauv paus plaub fab (√), qhov sib txawv ntawm qhov nthuav tawm 3 yog lub hauv paus kub (3), thiab ntxiv rau.
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Qhov no yuav ua rau me ntsis tsis meej pem, tab sis hauv cov xwm txheej no, koj tab tom nrhiav keeb kwm ntawm ob sab thaum ua haujlwm nrog cov lus piav qhia. Hauv lwm lo lus, koj tab tom ua qhov nthuav tawm rau ob sab thaum koj ua haujlwm nrog lub hauv paus. Saib hauv qab no:
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- Rau tus exponent, nrhiav lub hauv paus. Piv txwv: x2 = 49 → x = 4x √49
- Rau cov hauv paus hniav, nce. Piv txwv: x = 12 → x = 122
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Ntu 4 ntawm 5: Txhim Kho Koj Li Txuj Ci Algebra
Kauj Ruam 1. Siv cov duab los ua cov lus nug kom meej dua
Yog tias koj muaj teeb meem xav txog teeb meem algebra, sim siv daim duab lossis duab los qhia koj qhov kev ua zauv. Koj tseem tuaj yeem sim siv cov khoom ntawm lub cev (xws li thaiv lossis npib) yog tias koj muaj.
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Piv txwv, cia peb daws qhov sib npaug x + 2 = 3 siv lub xwmfab (☐)
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- x +2 = 3
- ☒+☐☐ =☐☐☐
- Hauv cov kauj ruam no, peb yuav rho 2 los ntawm ob sab los ntawm kev tshem 2 cov plaub fab (☐☐) los ntawm ob sab:
- ☒+☐☐-☐☐ =☐☐☐-☐☐
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= ☐, los yog x =
Kauj ruam 1.
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Raws li lwm qhov piv txwv, cia peb sim 2x = 4
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- ☒☒ =☐☐☐☐
- Hauv qib no, peb yuav faib ob tog los ntawm kev cais cov thawv ntawm txhua sab ua ob pawg:
- ☒|☒ =☐☐|☐☐
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=, sau x =
Kauj ruam 2.
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Kauj Ruam 2. Siv "kev nkag siab zoo" (tshwj xeeb rau cov lus nug dab neeg)
Thaum hloov cov teeb meem dab neeg mus rau algebra, sim tshuaj xyuas koj cov qauv los ntawm kev nkag mus rau qhov yooj yim rau koj qhov kev hloov pauv. Puas yog koj qhov sib npaug ua rau muaj kev nkag siab thaum x = 0? Thaum twg x = 1? Thaum twg x = -1? Nws yog qhov yooj yim los ua qhov yuam kev yooj yim ntawm kev sau p = 6d thaum koj txhais hais tias p = d/6, tab sis cov no yuav yooj yim rau pom yog tias koj ua nrawm, nkag siab zoo xyuas ntawm koj txoj haujlwm ua ntej txav mus.
Piv txwv li, peb tau hais tias thaj chaw ncaws pob yog 30 m ntev tshaj li qhov dav. Peb siv qhov sib npaug p = l + 30 los sawv cev rau qhov teeb meem no. Peb tuaj yeem tshawb xyuas yog tias qhov kev ua zauv no ua rau nkag siab los ntawm kev nkag yooj yim rau l. Piv txwv, yog tias thaj teb muaj qhov dav ntawm l = 10 m, qhov ntev yog 10 + 30 = 40 m. Yog tias qhov dav yog 30 m, qhov ntev yog 30 + 30 = 60 m, thiab ntxiv rau. Qhov kev ua zauv no ua rau nkag siab - peb cia siab tias daim teb no yuav muaj qhov ntev dua raws li qhov dav nce, yog li qhov kev ua zauv no ua rau nkag siab
Kauj Ruam 3. Nco ntsoov tias cov lus teb tsis yog ib txwm ua lej hauv algebra
Cov lus teb hauv algebra thiab lwm cov ntawv qib siab tsis yog ib txwm yooj yim, hloov tus lej. Tus lej no tuaj yeem yog zauv zauv, feem me me, lossis tus lej tsis muaj tseeb. Lub laij lej tuaj yeem pab koj nrhiav cov lus teb nyuaj no, tab sis nco ntsoov tias koj tus kws qhia ntawv yuav xav kom koj sau koj cov lus teb hauv daim ntawv meej, tsis yog daim ntawv zauv zauv nyuaj.
Piv txwv li, peb yuav ua kom yooj yim sib npaug algebraic rau x = 12507. Yog tias peb ntaus hauv 12507 hauv lub laij lej, peb yuav tau txais ntau qhov decimal qhov chaw (ntxiv rau, vim tias lub vijtsam lub laij lej tsis loj heev, lub laij lej tsis tuaj yeem tso saib txhua cov lus teb.) Hauv qhov no, peb yuav xav sau peb cov lus teb li tsuas yog 12507 lossis ua kom yooj yim cov lus teb los ntawm kev sau nws hauv cov ntawv sau tseg.
Kauj Ruam 4. Thaum koj muaj kev ntseeg siab nrog algebra yooj yim, sim ua qhov tseeb
Ib qho ntawm qhov muaj peev xwm algebraic nyuaj tshaj plaws ntawm txhua tus yog qhov sib txawv - ib hom kev luv luv rau tig txoj kab zauv nyuaj rau hauv cov ntawv yooj yim dua. Factoring yog cov ncauj lus ib nrab qib algebra, yog li txiav txim siab sab laj kab lus txuas saum toj no yog tias koj muaj teeb meem kev txawj nws. Hauv qab no tsuas yog qee qhov lus qhia ceev rau kev ua lej sib npaug:
- Qhov sib npaug ntawm daim ntawv ax + ba tau muab tso rau hauv a (x + b). Piv txwv: 2x + 4 = 2 (x + 2)
- Qhov sib npaug ntawm daim ntawv ax2 + bx yog qhov sib txawv rau cx ((a/c) x + (b/c)) qhov twg c yog tus lej loj tshaj plaws uas tuaj yeem faib sib npaug a thiab b. Ej.: 3 y2 + 12y = 3y (y + 4)
- Qhov sib npaug ntawm daim ntawv x2 + bx + c tau muab tso rau hauv (x + y) (x + z) qhov twg y × z = c thiab yx + zx = bx. Piv txwv: x2 4x + 3 = (x + 3) (x + 1).
Kauj Ruam 5. Xyaum, xyaum thiab xyaum
Kev vam meej hauv algebra (thiab lwm hom lej) yuav tsum siv zog ntau thiab rov ua dua. Tsis txhob txhawj xeeb - los ntawm kev mob siab rau hauv chav kawm, ua txhua yam koj tau ua, thiab nrhiav kev pab los ntawm koj tus kws qhia lossis lwm tus tub ntxhais kawm thaum koj xav tau, algebra yuav pib dhau los ua tus cwj pwm.
Kauj Ruam 6. Nug koj tus kws qhia ntawv kom pab koj nkag siab cov ntsiab lus algebraic nyuaj
Yog tias koj muaj teeb meem nkag siab algebra, tsis txhob txhawj xeeb - koj tsis tas yuav kawm nws ib leeg. Koj tus kws qhia ntawv yog thawj tus neeg koj yuav tsum tig mus rau cov lus nug. Tom qab chav kawm, ua siab ncaj nug koj tus kws qhia ntawv kom pab. Tus kws qhia ntawv zoo feem ntau yuav txaus siab piav qhia lub ntsiab lus ntawm hnub nyob hauv kev sib tham tom qab kawm ntawv thiab koj tus kws qhia ntawv tuaj yeem tuaj yeem muab cov ntaub ntawv xyaum ntxiv rau koj.
Yog tias, qee qhov laj thawj, koj tus kws qhia ntawv tsis tuaj yeem pab koj, nug nws txog nws txoj kev xaiv kawm ntxiv hauv koj lub tsev kawm ntawv. Ntau lub tsev kawm ntawv muaj qee yam kev kawm tom qab lawb ntawv uas tuaj yeem pab koj tau txais sijhawm ntxiv thiab saib xyuas koj xav tau kom pib paub koj li algebra. Nco ntsoov tias kev siv cov kev pab dawb muaj rau koj tsis muaj ib yam yuav txaj muag - nws yog lub cim qhia tias koj ntse txaus los daws koj cov teeb meem
Ntu 5 ntawm 5: Tshawb Nrhiav Cov Xaib Nruab Nrab
Kauj Ruam 1. Kawm paub kos kab x/y sib npaug
Cov duab tuaj yeem yog cov cuab yeej muaj txiaj ntsig hauv algebra vim tias lawv tso cai rau koj nthuav qhia cov tswv yim uas xav tau tus lej hauv daim duab ntawm kev nkag siab yooj yim. Feem ntau, hauv kev pib algebra, teeb meem teeb tsa tau txwv rau qhov sib npaug nrog ob qhov sib txawv (feem ntau yog x thiab y) thiab tau sawv cev hauv kab 2-D yooj yim nrog x-axis thiab y-axis. Nrog cov kab zauv no, txhua yam koj yuav tsum tau ua yog sau tus nqi rau x, tom qab ntawd tshawb rau y (lossis rov ua dua) kom tau txais ob tus lej uas dhau los ua tus lej ntawm kab ntawv.
- Piv txwv li, hauv kab zauv y = 3x, yog tias peb nkag mus rau 2 rau x, peb tau y = 6. Qhov no txhais tau tias lub ntsiab lus (2, 6) (ob kauj ruam mus rau sab xis los ntawm nruab nrab ntawm kab lus thiab rau qib nce los ntawm nruab nrab ntawm kab lus) yog ib feem ntawm kab lus ntawm kab zauv no.
- Qhov sib npaug ntawm daim ntawv y = mx + b (qhov twg m thiab b yog tus lej) muaj ntau heev hauv algebra yooj yim. Cov kab zauv no ib txwm muaj cov gradient lossis nqes hav m thiab sib tshuam y axis ntawm y = b.
Kauj Ruam 2. Kawm paub daws qhov tsis sib xws
Koj ua dab tsi thaum koj qhov kev ua zauv tsis muaj qhov kos npe sib npaug? Hloov tawm, tsis txawv ntawm qhov koj ib txwm ua. Rau qhov tsis sib xws, uas siv cov cim zoo li> ("ntau dua") thiab <("tsawg dua"), tsuas yog daws raws li ib txwm muaj. Koj yuav tawm cov lus teb uas tsawg dua lossis ntau dua li koj qhov sib txawv.
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Piv txwv li, nrog cov kab zauv 3> 5x - 2, peb yuav daws nws raws li peb xav ua ib txwm ua:
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- 3> 5x - 4x
- 5 x5
- 1> x, lub x <1.
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- Qhov no txhais tau tias txhua tus lej tsawg dua ib tus tuaj yeem yog tus nqi x. Hauv lwm lo lus, x tuaj yeem yog 0, -1, -2, thiab ntxiv rau. Yog tias peb ntsaws cov lej no rau hauv kab zauv rau x, peb ib txwm tau txais cov lus teb uas tsawg dua 3.
Kauj Ruam 3. Ua haujlwm ntawm cov zauv sib npaug
Ib qho ntawm cov ntsiab lus algebraic uas cov pib tshiab yuav muaj teeb meem nrog yog daws cov lej sib npaug. Lub xwmfab yog qhov sib npaug ntawm daim ntawv ax2 + bx + c = 0, qhov twg a, b, thiab c yog tus lej (tshwj tsis yog qhov tsis tuaj yeem yog 0). Cov kab zauv no raug daws los ntawm tus lej x = [-b +/- (b2 4ac)]/2a. Ua tib zoo - tus +/- kos npe txhais tau tias koj yuav tsum nrhiav cov lus teb rau ntxiv thiab rho tawm kom koj tuaj yeem muaj ob lo lus teb rau cov lus nug no.
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Piv txwv li, cia peb daws cov lej sib npaug 3x2 X 2x + 4x -1 = 0.
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- x = [-b +/- (b2 4ac)]/2a
- x = [-2 +/- (22 - 4(3)(-1))]/2(3)
- x = [-2 +/- (4- (-12))]/6
- x = [-2 +/- (16)]/6
- x = [-2 +/- 4]/6
- x = np - 1 thiab 1/3
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Kauj Ruam 4. Sim nrog cov kab ke sib npaug
Kev daws ntau dua ib qho kev ua zauv ib zaug tuaj yeem nyuaj heev, tab sis thaum koj ua haujlwm nrog cov lej sib npaug yooj yooj yim, nws tsis yog qhov nyuaj. Feem ntau, cov kws qhia lej algebra siv txoj hauv kev los daws cov teeb meem no. Thaum koj tab tom ua haujlwm nrog cov kab ke ntawm ob qhov kev ua zauv, cov kev daws teeb meem yog cov ntsiab lus ntawm kab ntawv uas ob kab kab sib tshooj sib tshuam.
- Piv txwv li, peb tab tom ua haujlwm nrog cov kab ke uas sib npaug y = 3x -2 thiab y = -x -6. Yog tias peb kos ob kab no ntawm kab ntawv, peb yuav tau txais ib kab uas nce los ntawm lub kaum ntse ntse, thiab ib uas nqes los ntawm lub kaum ntse ntse. Txij li cov kab no sib tshuam ntawm qhov chaw (-1, -5), ces lub ntsiab lus no yog kev daws teeb meem ntawm cov kab ke no.
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Yog tias peb xav tshuaj xyuas peb cov teeb meem, peb tuaj yeem ua li ntawd los ntawm ntsaws peb cov lus teb rau hauv kab zauv hauv kab ke - cov lus teb raug yuav yog "raug" rau ob qho kev ua zauv.
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- y = 4x - 3
- -5 = 3(-1) - 2
- -5 = -3 - 2
- -5 = -5
- y = -x - 6
- -5 = -(-1) - 6
- -5 = 1 - 6
- -5 = -5
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- Ob qhov sib npaug yog "tshuaj xyuas," yog li peb cov lus teb raug lawm!
Lub tswv yim
- Muaj ntau yam kev pab rau kev kawm algebra los ntawm internet. Piv txwv li, tshawb nrhiav "algebraic formula" hauv lub tshuab tshawb nrhiav. Muaj ntau qhov txiaj ntsig zoo uas yuav tshwm sim. Koj tseem tuaj yeem sim tshawb nrhiav los ntawm kev xaiv wikiHow cov lej lej. Muaj ntau cov ntaub ntawv tawm muaj, yog li pib tshawb nrhiav tam sim no!
- Ib qhov chaw zoo rau cov pib algebra yog khanacademy.com. Lub vev xaib pub dawb no muaj kaum ob qhov yooj yim-rau-ua raws cov lus qhia ntawm ntau yam ncauj lus, suav nrog algebra. Muaj cov vis dis aus rau txhua yam ntawm cov ncauj lus no, los ntawm cov hauv paus yooj yim mus rau cov ncauj lus qib hauv tsev kawm qib siab. Yog li tsis txhob ntshai tshawb Khan Academy cov ntaub ntawv thiab pib siv txhua qhov kev pab uas lub xaib tau muab!
- Tsis txhob hnov qab tias koj cov peev txheej zoo tshaj plaws thaum koj tab tom sim kawm algebra suav nrog cov neeg koj paub zoo. Nug koj cov phooj ywg lossis cov phooj ywg hauv chav kawm txog zaj lus kawg uas koj tsis nkag siab.
