Yuav ua li cas yog koob pheej ntawm lawv? Tus thawj kos npe rau ntawm lub hauv paus ntsiab lus ntawm koob pheej ntawm lawv thiab

"Koob pheej ntawm lawv" - ib lub npe uas cov menyuam kawm ntawv yog tseem nyob rau hauv tsev kawm ntawv. Nws nrog nws raws li nws tus "tsis sib xws". Cov ob lub tswv yim yog zoo txuas. Ntxiv mus, nrog lawv txuas cov nqe lus xws li kab zauv qhia tias yog leejtwg. Yog li ntawd yog dab tsi koob pheej ntawm lawv?

Lub tswvyim ntawm koob pheej ntawm lawv

Los ntawm no lub sij hawm yog xa mus rau hauv cov nqe lus nyob rau hauv cov ntaub ntawv uas muaj ib tug kos npe rau "=". Koob pheej ntawm lawv raug muab faib mus rau hauv txoj cai thiab tsis ncaj ncees lawm. Yog hais tias cov ntaubntawv povthawj siv yog tsim nyog es tsis txhob ntawm = <,>, thaum nws los txog rau tsis sib xws. Los ntawm txoj kev, cov thawj kos npe rau ntawm koob pheej ntawm lawv hais tias ob qhov chaw ntawm cov kev qhia yog zoo tib yam nyob rau hauv nws tshwm sim los yog cov ntaub ntawv.

Nyob rau hauv tas li ntawd mus rau lub tswvyim ntawm koob pheej ntawm lawv, lub tsev kawm ntawv kuj kawm lub npe "hais txog zauv koob pheej ntawm lawv". Nyob rau hauv daim ntawv no kom to taub ob numeric kab zauv uas sawv ntsug nyob rau ntawm ob sab ntawm lub = kos npe rau. Piv txwv li, 2 * 5 + 7 = 17. Ob leeg ntawm tus ncej yog muaj sib npaug.

Nyob rau hauv hais txog zauv cov nqe lus no hom yuav siv tau nkhaus rau txoj kev. Yog li ntawd, muaj 4 kev cai uas yuav tsum tau coj mus rau hauv tus account thaum xam xyuas cov ntsiab lus ntawm hais txog zauv kab zauv.

1. Yog hais tias lub nkag teb chaws tsis muaj koov, thaum ua hauj lwm yog ua los ntawm ib tug ntau dua kauj ruam: III → II → I. Yog hais tias muaj yog ob peb kauj ruam ib qeb, ces lawv sab laug mus rau sab xis.
2. Yog hais tias cov ntaub ntawv muaj kev zawm hniav, ces qhov kev txiav txim yog ua sau rau hauv, thiab ces noj mus rau hauv tus account lub kauj ruam. Tej zaum nyob rau hauv pab pawg yuav ua tau ntau qhov kev txiav txim.
3. Yog hais tias cov kev qhia yog muaj tuaj raws li ib feem, ces koj yuav tsum xub xam cov numerator, ces tus denominator, ces tus numerator muab faib los ntawm lub denominator.
4. Yog hais tias cov ntaub ntawv yog nested koov, ces tus thawj qhia yog soj ntsuam nyob rau hauv lub puab nkhaus.

Yog li ntawd, tam sim no nws yog ib qhov tseeb hais tias xws li koob pheej ntawm lawv. Nyob rau hauv lub neej yav tom ntej, lub tswvyim yuav tau los sib tham equation, tawv thiab cov hau kev ntawm lawv muab xam.

Properties txog zauv equations

Yuav ua li cas yog koob pheej ntawm lawv? Txoj kev tshawb no ntawm cov tswvyim no yuav tsum tau paub txog lub thaj chaw ntawm suav yog leej twg. Cov ntawv nram qab no qauv cia peb to taub zoo dua no lub npe. Ntawm cov hoob kawm, cov zog yog tsim rau txoj kev tshawb no ntawm kev kawm txog zauv nyob rau hauv high school.

1. Lub suav koob pheej ntawm lawv yuav tsis tau ua txhaum, yog hais tias ob qho tag nrho nws qhov chaw ntxiv tib yam xov tooj mus rau ib tug uas twb muaj lawm qhia.

Ib tug ↔ B = A + B = 5 + 5

2. Tsis txhob yuav ua txhaum kab zauv, yog tias ob tog yog multiplied los yog muab faib los ntawm tib lub xov tooj los yog kev hais lus, uas yog cov sib txawv ntawm xoom.

↔ P = O P = O ∙ 5 ∙ 5

P = O ↔ R 5 = Hais txog 5

3. Ntxiv rau ob tog ntawm tus neeg ntawm lub tib lub muaj nuj nqi, uas yuav ua rau kev txiav txim zoo rau tag nrho cov tau qhov tseem ceeb ntawm ib tug nce mus nce los, peb nrhiav tau ib tug tshiab kab zauv, uas yog sib npaug rau cov tseem cia nrog.

F (X) = Ψ (X ) ↔ F (X) + R (X) = Ψ (X) + R (X)

4. Ib lub sij hawm los yog kev qhia yuav tsum pauv mus rau sab tod los ntawm cov sib npaug zos kos npe rau, koj yuav tsum tau hloov lub kos npe rau.

X + Y = 5 - 20 ↔ X = Y - 20 - 5 ↔ X = Y - 25

5. multiply los yog faib rau ob sab los ntawm cov tib nuj nqi uas yog txawv los ntawm xoom thiab muaj lub ntsiab lus rau txhua tus nqi ntawm X los ntawm DHS, peb nrhiav tau ib tug tshiab kab zauv, uas yog sib npaug rau cov tseem cia nrog.

F (X) = Ψ (X ) ↔ F (X) ∙ R (X) = Ψ (X) ∙ R (X)

F (X) = Ψ (X ) ↔ F (X): G (X) = Ψ (X): G (X)

Cov kev cai tshaj tawm qhia cov neeg kawm ntawv ntawm lub hauv paus ntsiab lus ntawm koob pheej ntawm lawv, uas tshwm sim nyob rau hauv tej yam tej yam kev mob.

Lub tswvyim ntawm kev faib ua feem

Nyob rau hauv kev kawm txog zauv muaj xws li ib tug tshaj plaws raws li koob pheej ntawm lawv ntawm kev sib raug zoo. Nyob rau hauv cov ntaub ntawv no nws txhais tau tias kev txiav txim proportions. Yog hais tias lub seem A los B, ces cov no tus piv ntawm tus xov tooj ntawm ib tug mus B. Tus proportions xa mus rau lub koob pheej ntawm lawv ntawm ob kev sib raug zoo:

Tej zaum kev faib ua feem yog sau raws li nram no: A: B = C: D. Li no qhov yooj yim cov khoom teejtug proportions: A * D = D * C , qhov twg A thiab D - extremes proportions, thiab B thiab C - nruab nrab.

tawv

Yog leejtwg yog hu ua koob pheej ntawm lawv, uas yuav yog tseeb rau tag nrho cov tau qhov tseem ceeb ntawm lub zog uas yog ib feem ntawm txoj hauj lwm. Tawv yuav tuaj raws li alphabetic los yog numeric koob pheej ntawm lawv.

Identically sib npaug zos los yog kab zauv uas muaj ob tog ntawm tus tsis paub kuj tsis paub meej, uas muaj peev xwm equate lub ob qhov chaw ntawm ib tug tag nrho.

Yog hais tias peb kos cov kev hloov ntawm ib tug qhia los ntawm lwm tus, uas yog sib npaug zos rau, yog hais tias nws los txog rau lub qhia tias yog leejtwg pom. Nyob rau hauv cov ntaub ntawv no, koj yuav siv tau cov qauv ntawm abridged multiplication, cov kev cai ntawm xam thiab lwm yam neeg.

Yuav kom txo tau ib feem, nws yog tsim nyog los nqa tawm qhia tias yog leejtwg transformations. Piv txwv li, ib tug muab feem. Yuav kom tau txais kev tshwm sim, koj yuav tsum siv cov qauv ntawm abridged multiplication, factorization, simplification thiab yuav txo tau ntawm kev qhia tawm ntawm cov zauv feem.

Nws yog ib nqi xav tias yuav hais tias qhov no qhia yuav zoo tib yam thaum lub denominator yog tsis sib npaug zos rau 3.

5 txoj kev los ua pov thawj qhia tias yog leejtwg

Nyob rau hauv thiaj li yuav ua pov thawj rau leej twg, koj yuav tsum mus nqa tawm lub transformation ntawm kab zauv.

kuv txoj kev

Nws yog tsim nyog rau kev amounting mus hloov lub sab laug. Cov no rau sab xis, thiab peb yuav hais tias yog leejtwg yog muaj pov thawj.

II txoj kev

Tag nrho cov kev ua nyob rau hauv cov transformation ntawm kev qhia tshwm sim nyob rau hauv rau sab xis. Cov tshwm sim ntawm lub manipulation yog sab laug-tes sab. Yog hais tias tag nrho ob qho yeej zoo tib yam, tus neeg yog muaj pov thawj.

III txoj kev

"Transformation" tshwm sim nyob rau hauv tag nrho ob qho ntawm cov kev qhia. Yog hais tias raws li ib tug tshwm sim uas peb tau txais ob tug zoo tib qhov chaw, yog leejtwg yog muaj pov thawj.

IV txoj kev

Los ntawm cov sab laug ntawm txoj cai-hand yog rho tawm. Raws li ib tug tshwm sim ntawm sib npaug transformations yuav tsum tau txais pes tsawg. Tom qab ntawd peb yuav tham txog tus kheej ntawm kev qhia.

V txoj kev

Yog rho tawm los rau sab xis rau sab laug. Tag nrho amounting txia txo mus rau lub fact tias cov lus teb yog pes tsawg. Tsuas yog nyob rau hauv cov ntaub ntawv no peb yuav hais txog tus kheej ntawm koob pheej ntawm lawv.

Cov yooj yim zog ntawm tawv

Nyob rau hauv kev kawm txog zauv sib npaug zog yog feem ntau siv rau kom cov le caag txheej txheem. Vim qhov yooj yim txheej txheem ntawm xam xyuas ib tug algebraic neeg tej kab zauv yuav siv sij hawm feeb es siv sij hawm ntev.

• X + Y = Y + X
• X + (Y + C) = (X + Y) + C
• + X 0 = X
• X + (-hluav) = 0
• X ∙ (Y + C) = X X + Y ∙ ∙ C
• X ∙ (Y - C) X = ∙ Y - X ∙ C
• (X + Y) ∙ (C + E) = X + X C ∙ ∙ ∙ E + V C + V E ∙
• X + (Y + C) = X + Y + C
• X + (Y - C) = X + Y - C
• X - (Y + C) = X - Y - C
• X - (Y - C) = X - Y + C
• X ∙ Y = Y ∙ X
• ∙ X (Y ∙ C) = (X ∙ Y) ∙ C
• X 1 = X ∙
• ∙ X 1 / X = 1, nyob rau X ≠ 0

Cov qauv ntawm abridged npaug

Thaum nws cov tub ntxhais mis yog abridged npaug sib npaug. Lawv pab daws tau ntau yam teeb meem hauv kev kawm txog zauv vim hais tias ntawm nws cov simplicity thiab yooj yim ntawm kev siv.

• (A + B) ² = ² + 2 A ∙ ∙ B + B ² - square sum khub ntawm cov zauv;

• (A - B) ² = ² - A 2 ∙ ∙ B + B ² - ib tug khub ntawm squared sib txawv zauv;

• (C + B) ∙ (C - C) = C ² - B ² - sib txawv ntawm squares;

• (A + B) = ³ + 3 A ³ A ² ∙ ∙ Nyob rau hauv + 3 ∙ A ∙ B ² + B ³ - lub voos xwmfab nqi;

• (A - B) ³ = A ³ - A ² 3 ∙ ∙ B + A 3 ∙ ∙ V ² - V ³ - nyhav sib txawv;

• (P + B) ∙ (P ² - P ∙ B + B ²⁾ = F ³ NYOB RAU HAUV ³ + - sum ntawm cov ntsuas;

• (P - B) ∙ (P ² + P ∙ B + B ²⁾ = P ³ - B ³ - sib txawv ntsuas.

Abridged npaug mis yog feem ntau siv hais tias koj xav mus ua ib tug polynomial rau hauv lub niaj zaus daim ntawv los ntawm simplifying nws nyob rau hauv tag nrho cov tau txoj kev. Sawv cev los ntawm cov mis yuav tsum muaj pov thawj, tsuas qhib lub nkhaus thiab ua nyob rau hauv uas zoo sib xws cov lus.

kab zauv

Tom qab kev kawm rau lo lus nug, yog dab tsi kab zauv, koj yuav npaj mus rau lub kauj ruam tom ntej: dab tsi yog qhov equation. Nyob rau hauv kab zauv to taub koob pheej ntawm lawv, nyob rau cov tsis paub ntau tam sim no. Tshuaj ntawm cov kab zauv hu los nrhiav tau tag nrho cov qhov tseem ceeb ntawm ib tug nce mus nce los nyob rau hauv uas lub ob qhov chaw ntawm tag nrho cov kev qhia yuav tsum tau sib npaug. Tsis tas li ntawd, muaj hauj lwm nyob rau hauv uas nws yog tsis yooj yim sua mus nrhiav kev daws teeb meem ntawm kab zauv. Nyob rau hauv cov ntaub ntawv no peb hais tias muaj yog tsis muaj keeb kwm.

Raws li ib tug txoj cai, tsis paub hais tias koob pheej ntawm lawv raws li ib tug tshuaj rau muab cov zauv. Txawm li cas los, muaj mob qhov twg cov keeb kwm yog vector zog, thiab lwm yam khoom.

Cov kab zauv yog ib tug ntawm cov tseem ceeb tshaj plaws tswv yim nyob rau hauv kev kawm lej. Feem ntau ntawm cov kev thiab cov tswv yim muaj teeb meem tsis ntsuas los yog xam tej nqi. Yog li ntawd, koj yuav tsum muaj tus piv uas yuav los siav tag nrho cov tej yam kev mob ntawm neeg ua hauj lwm. Nyob rau hauv tus txheej txheem ntawm no piv zoo nkaus li kab zauv los yog kev sib npaug.

Feem ntau cov tshuaj ntawm koob pheej ntawm lawv nrog tsis paub hais tias thiaj li mus rau lub transformation ntawm ib tug complex kab zauv, thiab txo nws mus rau ib tug yooj yim zoo lawm. Nws yuav tsum tau nco ntsoov tias hloov dua siab tshiab yuav tsum tau nqa tawm nrog hwm rau ob leeg qhov chaw, txwv tsis pub cov zis yuav tig cov tsis ncaj ncees lawm no.

4, ib txoj kev los daws tau qhov equation

Los ntawm ib tug tov ntawm cov muab kab zauv to taub hloov lwm hais tias yog sib npaug rau cov thawj. Xws li ib tug hloov yog hu ua tus qhia tias yog leejtwg pom. Yuav kom daws tau cov kab zauv, koj yuav tsum siv ib qho ntawm cov hau kev.

1. Ib qhia yog hloov los ntawm lwm, uas tas yuav zoo tib yam rau cov thawj. Piv txwv li: (3 ∙ x + 3) ² = 15 + 10 x ∙. Qhov no qhia tej zaum yuav hloov dua siab tshiab rau 9 ∙ x ² + 18 x ∙ = 15 + 9 + 10 x ∙.

2. Cov kev hloov ntawm cov neeg sib npaug zos rau cov tsis paub hais tias los ntawm ib sab mus rau lwm yam. Nyob rau hauv cov ntaub ntawv no nws yog tsim nyog los hloov cov cim kom raug. Lub slightest yuam kev puam tsuaj tag nrho cov ua hauj lwm ua. Raws li ib qho piv txwv, noj yav dhau los "qauv".

9 ∙ x ² + 12 x ∙ + 4 = 15 + 10 x ∙

9 ∙ x ² + x 12 + 4 ∙ - ∙ x 15 - 10 = 0

9 ∙ x ² - x 3 ∙ - 6 = 0

Ces tus kab zauv solved siv cov discriminant.

3. Muab ob sab ntawm ib tug sib npaug zos xov tooj los yog qhia hais tias tsis yog sib npaug zos rau 0. Txawm li cas los, nws yog ib nqi recalling tias thaum tus tshiab equation tsis yog sib npaug rau cov koob pheej ntawm lawv ua ntej qhov kev hloov, ces tus nqi ntawm cov hauv paus hniav yuav txawv heev.

4. squaring ob tog ntawm lub kab zauv. Qhov no txoj kev yog tsuas zoo kawg li, tshwj xeeb tshaj yog thaum koob pheej ntawm lawv yog ib tug irrational qhia, uas yog, lub square hauv paus ntawm qhov qhia nyob rau hauv nws. Muaj yog ib tug caveat: yog hais tias koj tsim ib qho kev ua nyob rau hauv txawm degree, ces tej zaum yuav tshwm sim extraneous cov hauv paus hniav, uas distort cov essence ntawm txoj hauj lwm. Thiab yog hais tias nws yog tsis ncaj ncees lawm mus coj ib tug hauv paus, ces lub ntsiab lus ntawm cov nqe lus nug nyob rau hauv qhov teeb meem yog tsis meej. QAUV: │7 ∙ h│ = 35 → 1) 7 ∙ x = 35 thiab 2) - 7 ∙ x = 35 → kab zauv yuav yuav daws tau kom raug.

Yog li ntawd, qhov no tsab xov xwm yog hais txog cov ntsiab lus raws li qhov sib npaug thiab yog leej twg. Lawv tag nrho cov los ntawm lub "koob pheej ntawm lawv" ntawm lub tswvyim. Vim lub ntau yam ntawm cov kab zauv sib npaug rau hauv kev daws ntawm tej yam teeb meem mus rau ib tug loj raws li thawm.