Ib qho plaub fab sib npaug yog qhov sib npaug uas nws qib siab tshaj plaws yog 2 (sib npaug). Muaj peb txoj hauv kev tseem ceeb los daws qhov sib npaug sib npaug: ntsuas qhov sib npaug ntawm plaub fab yog tias koj tuaj yeem ua tau, siv cov lej sib npaug, lossis ua kom tiav cov xwm txheej. Yog tias koj xav ua tus tswv peb txoj hauv kev no, ua raws cov theem no.
Kauj ruam
Txoj Kev 1 ntawm 3: Kev Sib Piv Factoring
Kauj Ruam 1. Muab tag nrho cov sib npaug sib npaug thiab txav lawv mus rau ib sab ntawm qhov sib npaug
Thawj kauj ruam rau kev ntsuas qhov sib npaug yog txav txhua qhov sib npaug sib txawv mus rau ib sab ntawm qhov sib npaug, nrog x2yog qhov zoo. Txhawm rau hloov pauv, ntxiv lossis rho tawm txhua qhov hloov pauv x2, x, thiab tus lej (cov lej), txav lawv mus rau lwm sab ntawm qhov sib npaug kom tsis muaj dab tsi nyob ntawm lwm sab. Thaum lwm sab tsis muaj qhov hloov pauv ntxiv, sau 0 ib sab ntawm qhov kos npe sib npaug. Nov yog yuav ua li cas:
- 2x ua2 8 - 4x = 3 - x2
- 2x ua2 +xwm2 -8x -3x -4 = 0
- 3 x ygo2 4x - 11 = 0
Kauj Ruam 2. Ntsuas qhov sib npaug no
Txhawm rau ntsuas qhov sib npaug no, koj yuav tsum siv qhov x2 (3) thiab qhov tseem ceeb (-4), muab lawv sib ntxiv thiab ntxiv lawv kom haum rau qhov sib txawv hauv nruab nrab, (-11). Nov yog yuav ua li cas:
- 3 x ygo2 muaj tsuas yog ib qho ua tau uas yog, 3x thiab x, koj tuaj yeem sau lawv hauv kab lus: (3x +/-?) (x +/-?) = 0.
- Tom qab ntawd, siv cov txheej txheem tshem tawm mus rau hauv 4 txhawm rau nrhiav cov khoom lag luam uas tawm los -11x. Koj tuaj yeem siv cov khoom ntawm 4 thiab 1, lossis 2 thiab 2, vim tias thaum koj muab ob qho tib si koj tau txais 4. Tab sis nco ntsoov tias ib tus lej yuav tsum tsis zoo vim qhov tshwm sim yog -4.
- Sim (3x + 1) (x - 4). Thaum koj suav nws, qhov tshwm sim yog - 3x2 -12x +x -4. Yog tias koj ua ke cov kev hloov pauv -12 x thiab x, qhov tshwm sim yog -11x, uas yog koj tus nqi nruab nrab. Koj tsuas yog tau txiav txim siab qhov kev ua zauv plaub fab.
- Piv txwv, cia peb sim ua qhov tseeb ntawm lwm yam khoom: (3x -2) (x +2) = 3x2 6x +4x -2. Yog tias koj ua ke cov kev hloov pauv, qhov tshwm sim yog 3x2 -4x -4. Txawm hais tias qhov tseem ceeb ntawm -2 thiab 2 thaum sib tw ua cov khoom -4, lub ntsiab lus tsis zoo ib yam vim tias koj xav tau tus nqi ntawm -11x hloov -4x.
Kauj Ruam 3. Xav tias txhua kab lus sib piv yog xoom hauv qhov sib npaug sib txawv
Qhov no yuav qhia koj pom 2 x qhov muaj txiaj ntsig uas yuav ua rau koj qhov kev ua zauv xoom. Koj tau txheeb xyuas koj qhov kev ua zauv, yog li txhua yam koj yuav tsum ua yog xav txog kev suav hauv txhua kab lus sib npaug xoom. Yog li, koj tuaj yeem sau 3x + 1 = 0 thiab x - 4 = 0.
Kauj Ruam 4. Kuaj txhua qhov zauv sib cais
Hauv ib qho zauv sib npaug, muaj 2 qhov tseem ceeb rau x. Txhim kho txhua qhov kev ua zauv cais los ntawm kev hloov pauv thiab sau 2 cov lus teb rau x, zoo li no:
-
Daws teeb meem 3x + 1 = 0
- 3x = -1….. los ntawm kev rho tawm
- 3x/3 = -1/3….. los ntawm kev faib
- x = -1/3….. los ntawm kev ua kom yooj yim
-
X -4x = 0
x = 4….. los ntawm kev rho tawm
- x = (-1/3, 4)….. los ntawm kev ua ob peb lo lus teb tau cais, lub ntsiab lus x = -1/3 lossis x = 4 ob qho tib si yuav raug.
Kauj Ruam 5. Kos x = -1/3 hauv (3x + 1) (x -4) = 0:
Yog li peb tau txais (3 [-1/3] + 1) ([-1/3]-4)? =? 0….. los ntawm kev hloov pauv (-1 + 1) (-4 1/3)? =? 0….. los ntawm kev yooj yim (0) (-4 1/3) = 0….. los ntawm kev sib npaug Yog li, 0 = 0….. Yog, x = -1/3 yog qhov tseeb.
Kauj Ruam 6. Kos x = 4 hauv (3x + 1) (x - 4) = 0:
Yog li peb tau txais (3 [4] + 1) ([4] - 4)? =? 0….. los ntawm kev hloov pauv (13) (4 - 4)? =? 0….. los ntawm kev yooj yim (13) (0) = 0….. los ntawm kev sib npaug Yog li, 0 = 0….. Yog, x = 4 kuj muaj tseeb thiab.
Yog li, tom qab tshawb xyuas cais, ob qho lus teb raug thiab tuaj yeem siv ua qhov sib npaug
Txoj Kev 2 ntawm 3: Siv Cov Qauv Zauv
Kauj Ruam 1. Muab tag nrho cov sib npaug sib npaug thiab txav lawv mus rau ib sab ntawm qhov sib npaug
Tsiv tag nrho cov kev hloov pauv mus rau ib sab ntawm qhov sib npaug, nrog tus nqi ntawm qhov sib txawv x2 zoo. Sau cov kev hloov pauv nrog cov lej nthuav tawm, yog li x2 sau ua ntej, ua raws los ntawm kev hloov pauv, thiab tsis tu ncua. Nov yog yuav ua li cas:
- 4x ua2 5x - 13 = x - 4x2 -5
- 4x ua2 -x ib2 5x - 13 +5 = 0
- 3 x ygo2 -5x - 8 = 0
Kauj Ruam 2. Sau cov lej sib npaug
Cov lej piv txwv yog: b ± b2−4ac2a { displaystyle { frac {-b / pm { sqrt {b^{2} -4ac}}} {2a}}
Kauj Ruam 3. Txheeb xyuas qhov muaj nuj nqis ntawm a, b, thiab c los ntawm qhov ua zauv sib npaug
Qhov sib txawv a yog qhov coefficient x2, b yog qhov sib npaug ntawm qhov sib txawv x, thiab c yog qhov tsis tu ncua. Rau qhov sib npaug 3x2 -5x -8 = 0, a = 3, b = -5, thiab c = -8. Sau tag nrho peb qho.
Kauj Ruam 4. Hloov qhov tseem ceeb ntawm a, b, thiab c hauv kab zauv
Thaum koj paub peb qhov tseem ceeb sib txawv, ntsaws lawv rau hauv qhov sib npaug zoo li no:
- {-b +/- √ (b2 4ac)}/2
- {-(-5) +/-√ ((-5)2 - 4(3)(-8))}/2(3) =
- {-(-5) +/-√ ((-5)2 - (-96))}/2(3)
Kauj Ruam 5. Ua cov laij lej
Thaum koj tau nkag mus rau tus lej, ua qee qhov lej los ua kom yooj yim rau qhov zoo lossis tsis zoo kos npe, muab sib npaug, lossis faib cov lej ntxiv. Nov yog yuav ua li cas:
- {-(-5) +/-√ ((-5)2 - (-96))}/2(3) =
- {5 +/-√(25 + 96)}/6
- {5 +/-√(121)}/6
Kauj Ruam 6. Yooj yim rau cov hauv paus cag
Yog tias tus lej hauv qab lub hauv paus square yog lub xwmfab zoo meej, koj tau txais tus lej tag nrho. Yog tias tus lej tsis yog lub xwmfab zoo tshaj, ua rau nws yooj yim hauv paus daim ntawv. Yog tias tus lej tsis zoo thiab koj ntseeg tias nws yuav tsum tsis zoo, lub hauv paus tus nqi yuav nyuaj. Hauv qhov piv txwv no, (121) = 11. Koj tuaj yeem sau x = (5 +/- 11)/6.
Kauj Ruam 7. Nrhiav cov lus teb zoo thiab tsis zoo
Thaum koj tau tshem daim phiaj xwm txheej hauv paus, koj tuaj yeem ua haujlwm koj txoj hauv kev kom pom qhov txiaj ntsig thiab qhov tsis zoo rau x. Tam sim no koj muaj (5 +/- 11)/6, koj tuaj yeem sau 2 cov lus teb:
- (5 + 11)/6
- (5 - 11)/6
Kauj Ruam 8. Ua kom tiav cov lus teb zoo thiab tsis zoo
Ua laij lej:
- (5 + 11)/6 = 16/6
- (5-11)/6 = -6/6
Kauj Ruam 9. Yooj Yim
Txhawm rau ua kom yooj yim rau txhua lo lus teb, faib los ntawm tus lej loj tshaj uas tuaj yeem faib ob tus lej. Faib thawj feem ntawm 2 thiab faib qhov thib ob los ntawm 6, thiab koj tau pom tus nqi x.
- 16/6 = 8/3
- -6/6 = -1
- x = (-1, 8/3)
Txoj Kev 3 ntawm 3: Ua kom tiav Square
Kauj Ruam 1. Tsiv tag nrho cov kev hloov pauv mus rau ib sab ntawm qhov sib npaug
Nco ntsoov tias a lossis sib txawv x2 zoo. Nov yog yuav ua li cas:
- 2x ua2 9 = 12 x = np
-
2x ua2 -12x -9 = 0
Hauv qhov sib npaug no, sib txawv a yog 2, sib txawv b yog -12, thiab sib txawv c yog -9
Kauj Ruam 2. Txav mus rau qhov hloov pauv lossis tas c mus rau lwm sab
Cov lej yog cov lej uas tsis muaj qhov sib txawv. Tsiv mus rau sab xis ntawm kab zauv:
- 2x ua2 -12x -9 = 0
- 2x ua2 -12x = 9
Kauj Ruam 3. Sib faib ob sab los ntawm qhov sib npaug a lossis qhov sib txawv x2.
Yog x2 tsis muaj qhov sib txawv thiab qhov sib npaug yog 1, koj tuaj yeem hla cov kauj ruam no. Hauv qhov no, koj yuav tsum faib txhua qhov sib txawv los ntawm 2, zoo li no:
- 2x ua2/2 - 12x/2 = 9/2 =
- x kev2 -6x = 9/2
Kauj Ruam 4. Sib faib b los ntawm 2, square nws, thiab ntxiv qhov tshwm sim rau ob sab
Tus nqi ntawm b hauv qhov piv txwv no yog -6. Nov yog yuav ua li cas:
- -6/2 = -3 =
- (-3)2 = 9 =
- x kev2 6x + 9 = 9/2 + 9
Kauj Ruam 5. Yooj yim rau ob sab
Ntsuas qhov sib txawv ntawm sab laug kom tau txais (x-3) (x-3) lossis (x-3)2. Ntxiv qhov tseem ceeb rau sab xis kom tau 9/2 + 9 lossis 9/2 + 18/2, uas yog 27/2.
Kauj Ruam 6. Nrhiav lub hauv paus rau ob sab
Square hauv paus ntawm (x-3)2 yog (x-3). Koj tuaj yeem sau lub hauv paus square ntawm 27/2 raws li √ √ (27/2). Yog li, x - 3 = ± √ (27/2).
Kauj Ruam 7. Yooj yim rau cov hauv paus hniav thiab nrhiav tus nqi x
Kom yooj yim dua √ √ (27/2), nrhiav lub xwmfab zoo tshaj ntawm tus lej 27 thiab 2 lossis tus lej ntawd. Cov xwm txheej zoo tshaj plaws ntawm 9 tuaj yeem nrhiav tau hauv 27 vim tias 9 x 3 = 27. Txhawm rau coj 9 tawm ntawm cov hauv paus cag, coj 9 tawm ntawm lub hauv paus thiab sau 3, cov hauv paus plaub fab, sab nraum lub hauv paus square. Tawm qhov seem 3 hauv tus lej ntawm cov feem hauv qab cov hauv paus hauv paus, txij li 27 tsis ua haujlwm tawm ntawm txhua yam, thiab sau 2 hauv qab no. Tom qab ntawd, txav mus tas li 3 ntawm sab laug ntawm kab zauv mus rau sab xis, thiab sau koj ob qho kev daws teeb meem rau x:
- x = 3 +(√6)/2
- x = 3 - (√6)/2)
Lub tswv yim
- Raws li koj tuaj yeem pom, cov cim hauv paus yuav tsis ploj mus kiag li. Yog li, cov lej sib txawv tsis tuaj yeem ua ke (vim tias lawv tsis sib npaug). Tsis muaj lub ntsiab lus hauv kev cais nws mus rau qhov zoo lossis tsis zoo. Txawm li cas los xij, peb tuaj yeem faib nws los ntawm tib yam, tab sis XWB yog tias cov xwm txheej zoo ib yam rau ob qho tib si THIAB hauv paus coefficient
- Yog tias tus lej hauv qab lub hauv paus tsis yog lub xwmfab zoo, tom qab ob peb kauj ruam dhau los sib txawv me ntsis. Nov yog qhov piv txwv:
- Yog tias b yog tus lej sib npaug, cov qauv ua: {-(b/2) +/- (b/2) -ac}/a.
