Ua kom tiav cov duab plaub yog cov txheej txheem muaj txiaj ntsig zoo los pab koj muab cov lej sib npaug sib npaug rau hauv daim ntawv zoo, uas ua rau lawv pom yooj yim lossis tseem daws tau. Koj tuaj yeem ua tiav cov xwm txheej los tsim cov qauv sib npaug sib npaug ntau dua lossis txawm tias daws cov lej sib npaug. Yog koj xav paub yuav ua li cas, ua raws cov theem no.
Kauj ruam
Ntu 1 ntawm 2: Hloov Cov Kev Sib Tw Ib Leeg rau Kev Ua Plaub Ntug
Kauj Ruam 1. Sau kab zauv
Piv txwv tias koj xav daws qhov sib npaug hauv qab no: 3x2 4x + 5.
Kauj Ruam 2. Tshem tawm cov coefficients ntawm cov lej sib npaug los ntawm thawj ob ntu
Txhawm rau kom tau tus lej 3 tawm ntawm thawj ob ntu, tsuas yog siv tus lej 3 tawm thiab muab nws tso rau sab nraum cov khoom sib faib, faib txhua feem los ntawm 3. 3x2 faib 3 x2 thiab 4x faib los ntawm 3 yog 4/3x. Yog li, qhov sib npaug tshiab dhau los: 3 (x2 - 4/3x) + 5. Tus lej 5 tseem nyob sab nraud vim nws tsis faib los ntawm tus lej 3.
Kauj Ruam 3. Muab qhov thib ob faib ua 2 thiab muab faib ua plaub fab
Qhov thib ob lossis qhov uas paub tias yog b hauv qhov kev ua zauv yog 4/3. Muab faib ua ob. 4/3 2, lossis 4/3 x 1/2, sib npaug 2/3. Tam sim no, square ntu no los ntawm kev ntsuas qhov feem ntawm tus lej thiab cov zauv. (2/3)2 Luas = 4/9 Sau nws cia.
Kauj Ruam 4. Ntxiv thiab rho tawm cov ntu no los ntawm kev ua zauv
Koj yuav xav tau qhov tshwj xeeb no kom tau qhov sib npaug rov qab rau lub xwmfab zoo meej. Txawm li cas los xij, koj yuav tsum rho lawv los ntawm qhov seem ntawm qhov sib npaug kom ntxiv lawv. Txawm hais tias, nws zoo li koj yuav rov qab mus rau koj thawj qhov sib npaug. Koj qhov sib npaug zoo li no: 3 (x2 4/3 x + 4/9 - 4/9) + 5.
Kauj Ruam 5. Tshem tawm qhov koj rho tawm los ntawm cov kab zauv
Txij li thaum koj muaj qhov sib npaug ntawm 3 sab nraum cov kab lus, koj tsis tuaj yeem tsuas yog tso tawm -4/9. Koj yuav tsum muab nws suav nrog 3 ua ntej. -4/9 x 3 = -12/9, lossis -4/3. Yog tias koj muaj qhov sib npaug ntawm 1 hauv ntu x2, tom qab ntawd koj tuaj yeem hla cov kauj ruam no.
Kauj Ruam 6. Hloov ib feem hauv cov kab zauv mus rau lub xwmfab zoo meej
Tam sim no, muaj 3 (x2 -4/3x +4/9) hauv cov kab ntawv. Koj twb tau sim kom tau 4/9, uas yog lwm txoj hauv kev kom ua tiav cov xwm txheej. Yog li koj tuaj yeem sau nws li: 3 (x - 2/3)2. Txhua yam koj yuav tsum ua yog faib qhov thib ib nrab thiab tshem qhov thib peb. Koj tuaj yeem tshawb xyuas koj txoj haujlwm los ntawm kev sib npaug nws thiab los nrog thawj peb ntu ntawm qhov sib npaug.
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3 (x - 2/3)2 =
Ua kom tiav Square Step 6Bullet1 - 3 (x - 2/3) (x -2/3) =
- 3 [(xwm2 -2/3x -2/3x + 4/9)]
- 3 (xws2 4x - 4x + 9/9
Kauj Ruam 7. Muab cov khoom sib txuas
Tam sim no muaj ob qhov txuas lossis tus lej uas tsis muaj qhov sib txawv. Tam sim no, koj muaj 3 (x - 2/3)2 - 4/3 + 5. Txhua yam koj yuav tsum ua yog ntxiv -4/3 thiab 5 kom tau 11/3. Koj ntxiv lawv los ntawm kev sib piv cov lej: -4/3 thiab 15/3, thiab tom qab ntawd ntxiv cov lej kom koj tau 11 thiab tawm ntawm cov lej 3.
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-4/3 + 15/3 = 11/3.
Ua kom tiav Square Step 7Bullet1
Kauj Ruam 8. Sau kab zauv hauv daim duab plaub
Koj tau ua tiav. Qhov zauv kawg yog 3 (x - 2/3)2 +11/3. Koj tuaj yeem tshem tawm qhov coefficient ntawm 3 los ntawm kev faib ob sab ntawm qhov sib npaug kom tau txais (x - 2/3)2 +11/9. Koj tau ua tiav qhov kev ua zauv rau hauv daim duab plaub, uas yog a (x - h)2 +k, tus qhov twg k sawv cev rau qhov tsis tu ncua.
Ntu 2 ntawm 2: Daws Sib Piv Plaub Ntug
Kauj Ruam 1. Sau cov lus nug
Piv txwv tias koj xav daws qhov sib npaug hauv qab no: 3x2 4x + 5 = 6
Kauj Ruam 2. Muab cov cim uas twb muaj lawm tso tso rau ntawm sab laug ntawm kab zauv
Qhov tsis tu ncua yog ib tus lej uas tsis muaj qhov sib txawv. Hauv qhov teeb meem no, qhov tsis tu ncua yog 5 ntawm sab laug thiab 6 ntawm sab xis. Yog tias koj xav txav 6 mus rau sab laug, koj yuav tsum rho ob sab ntawm qhov sib npaug los ntawm 6. Qhov seem yog 0 ntawm sab xis (6-6) thiab -1 ntawm sab laug (5-6). Qhov sib npaug ua: 3x2 4x - 1 = 0.
Kauj Ruam 3. Tso tawm cov coefficient ntawm qhov sib txawv sib npaug
Hauv qhov teeb meem no, 3 yog tus coefficient ntawm x2. Kom tau tus lej 3, tsuas yog muab tus lej 3, thiab faib txhua feem los ntawm 3. Yog li, 3x2 3 = x os2, 4x 3 = 4/3x, and 13 = 1/3. Qhov sib npaug ua: 3 (x2 + 4x - 1/3) = 0.
Kauj Ruam 4. Sib faib los ntawm qhov tas li koj nyuam qhuav rho tawm
Qhov no txhais tau tias koj tuaj yeem tshem qhov coefficient 3. Txij li thaum koj twb tau faib txhua feem los ntawm 3, koj tuaj yeem tshem tus lej 3 yam tsis cuam tshuam rau kev ua zauv. Koj qhov sib npaug ua x2 + 4x - 1/3 = 0
Kauj Ruam 5. Muab qhov thib ob faib ua 2 thiab muab faib ua plaub fab
Tom ntej no, siv qhov thib ob, 4/3, lossis ntu b, thiab faib nws los ntawm 2. 4/3 2 lossis 4/3 x 1/2, sib npaug 4/6 lossis 2/3. Thiab 2/3 sib npaug rau 4/9. Thaum koj tau muab nws ua plaub fab, koj yuav tsum tau sau nws ntawm sab laug thiab sab xis ntawm qhov sib npaug vim tias koj tab tom ntxiv ntu tshiab. Koj yuav tsum sau nws ntawm ob sab kom sib npaug. Qhov sib npaug ua x2 4x + 3 x + 2/32 - 1/3 = 2/32
Kauj Ruam 6. Tsiv qhov pib tsis tu ncua mus rau sab xis ntawm kab zauv thiab ntxiv nws mus rau qhov xwm txheej ntawm koj tus lej
Tsiv qhov pib tsis tu ncua, -1/3, mus rau sab xis, ua nws 1/3. Ntxiv cov xwm txheej ntawm koj tus lej, 4/9 lossis 2/32. Nrhiav tus lej sib koom ua ke ntxiv 1/3 thiab 4/9 los ntawm kev faib cov zauv sab saum toj thiab hauv qab ntawm 1/3 los ntawm 3. 1/3 x 3/3 = 3/9. Tam sim no ntxiv 3/9 thiab 4/9 kom tau 7/9 ntawm sab xis ntawm kab zauv. Qhov sib npaug ua: x2 4x + 3 x + 2/32 = 4/9 + 1/3 ces x2 4x + 3 x + 2/32 = 7/9.
Kauj Ruam 7. Sau rau sab laug ntawm kab zauv ua lub xwmfab zoo meej
Txij li koj twb tau siv cov mis los nrhiav qhov uas ploj lawm, qhov nyuaj tau hla mus. Txhua yam koj yuav tsum ua yog muab x thiab ib nrab tus nqi ntawm qhov thib ob coefficient hauv cov ntawv thiab muab piv rau nws, piv txwv li: (x + 2/3)2. Nco ntsoov tias qhov kev txiav txim plaub fab zoo yuav muab peb ntu: x2 4x + 3 x + 9/4. Qhov sib npaug ua: (x + 2/3)2 = 7/9.
Kauj Ruam 8. Square cag ntawm ob sab
Ntawm sab laug ntawm kab zauv, lub hauv paus square ntawm (x + 2/3)2 yog x + 2/3. Ntawm sab xis ntawm kab zauv, koj yuav tau txais +/- (√7)/3. Lub hauv paus square ntawm tus lej, 9, yog 3, thiab lub hauv paus square ntawm 7 yog 7. Nco ntsoov sau +/- vim tias cov hauv paus hauv paus tuaj yeem ua qhov zoo lossis tsis zoo.
Kauj Ruam 9. Txav mus rau qhov hloov pauv
Txhawm rau txav qhov sib txawv x, tsuas yog txav qhov 2/3 mus rau sab xis ntawm kab zauv. Tam sim no, koj muaj ob lo lus teb tau rau x: +/- (√7)/3 - 2/3. Nov yog koj ob lo lus teb. Koj tuaj yeem tso nws ib leeg lossis nrhiav tus nqi ntawm cov hauv paus plaub ntawm 7 yog tias koj yuav tsum sau cov lus teb yam tsis muaj lub hauv paus cag.
Lub tswv yim
- Nco ntsoov sau +/- hauv qhov chaw tsim nyog, txwv tsis pub koj yuav tsuas tau txais ib lo lus teb.
- Txawm tias tom qab koj paub cov lej sib npaug, xyaum ua kom tiav cov xwm txheej ib txwm los ntawm kev ua pov thawj cov lej sib npaug lossis daws qee cov teeb meem. Txoj kev ntawd, koj yuav tsis hnov qab txoj hauv kev thaum koj xav tau.
