Kuyini ukulingana? Uphawu lokuqala izimiso zokulingana kanye

"Ukulingana" - ngesihloko ukuthi abafundi zisekhona esikoleni sabaqalayo. It iya kuye ngokuthi "ukungalingani" yakhe. Lezi imiqondo kokubili kuhlobene kakhulu. Ngaphezu kwalokho, nabo exhumene lafana kwesibalo ungubani. Ngakho-ke yini ukulingana?

Umqondo ukulingana

Ngalokhu eside ubizwa izitatimende irekhodi ukuthi kukhona uphawu "=". Ukulingana zihlukaniswe phakathi kokulungile nokungalungile. Uma ukuqopha esikhundleni = kuwufanele <,>, uma kuziwa ukungalingani. By the way, kuqubuka ukulingana uthi izingxenye ezimbili le nkulumo ezifanayo yi yayo noma irekhodi.

Ngaphezu nomqondo ukulingana, isikole naye wafundelwa isihloko "ukulingana zezinombolo". Ngaphansi kwalesi sitatimende ukuqonda izenzo ezimbili zokubonakaliswa yezinombolo ukuthi ume zombili = uphawu. Ngokwesibonelo, 2 * 5 + 7 = 17. Zombili okuthunyelwe bayalingana.

Ngamagama zezinombolo lolu hlobo zingasetshenziswa kubakaki ezithinta inqubo. Ngakho, kukhona 4 imithetho okufanele kucatshangelwe lapho kubalwa imiphumela zenombolo.

1. Uma entry kungekho abakaki, kuyilapho imisebenzi eyenziwa kusukela isinyathelo ephakeme: III → II → I. Uma kukhona izinyathelo ezimbalwa isigaba esisodwa ke basuke kwesokunxele kuya kwesokudla.
2. Uma irekhodi has besokunxele ke isenzo wenziwa abakaki, bese kucatshangelwa izinyathelo. Mhlawumbe kubakaki kuyoba isenzo esiningi.
3. Uma inkulumo ethi umelwe ingxenyenamba ke kuzomele uqale ukubala numerator, ke zifana, ke numerator yahlukaniswa zifana.
4. Uma amarekhodi abakaki isichazi ke inkulumo ethi wokuqala esikalini amabhrakhethi kwangaphakathi.

Ngakho, manje kuyacaca ukuthi ukulingana ezinjalo. Esikhathini esizayo, umqondo kuzoxoxwa equation, ubunikazi kanye nezindlela ukubala kwabo.

Izakhiwo zibalo zezinombolo

Kuyini ukulingana? Ucwaningo lo mqondo kudinga ulwazi property ubunikazi zezinombolo. Umbhalo amafomula elandelayo esisiza ukuba siqonde kangcono lesi sihloko. Yiqiniso, lezi izakhiwo ekahle cwaningo wezibalo esikoleni esiphakeme.

1. ukulingana zezinombolo ngeke ephulwa uma kokubili ezingxenyeni zalo ungeze inombolo efanayo ekuboniseni ekhona.

A ↔ B = A + B = 5 + 5

2. Musa ephulwa equation, uma zombili ziziningi noma zihlukaniswe inombolo efanayo noma isisho, okuyizinto sihluke zero.

↔ P = O P = O ∙ 5 ∙ 5

P = O ↔ R 5 = Mayelana 5

3. Ukungeza zombili izinhlangothi ungubani engenawo umsebenzi ofanayo, ukuthi kunengqondo ngaso sonke amagugu kungenzeka kwenombolo, sithola equation omusha, okulingana original.

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

4. Noma yikuphi eside noma isisho angadluliselwa kolunye uhlangothi setshwayo, uzodinga ukushintsha uphawu.

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

5. nande noma bahlukanise zombili nge umsebenzi ofanayo ukuthi lihlukile zero nokuba sisho okuthile ukubaluleka ngamunye X kusukela DHS, sithola equation omusha, okulingana original.

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

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

Le mithetho ngokucacile ukhombise degree isimiso ukulingana, ongagcini ngaphansi kwezimo ezithile.

Umqondo Ingxenye

Esifundweni sezibalo kukhona into efana nokulingana ubudlelwane. Kulokhu-ke kusho sokunquma ngezabelo. Uma esigabeni A to B, bese umphumela kuba isilinganiso inani ku-A kuya B. ngezabelo wabhekisela nokulingana ubudlelwane ezimbili:

Ngezinye izikhathi ingxenye kulotshiwe kanje: A: B = C: D. Yingakho eziyisisekelo impahla ngezabelo: A * D = D * C , lapho A no D - ukweqisa ngezabelo, futhi B no-C - ophansi.

ubunikazi

Identity ibizwa ngokuthi ukulingana, okuzoba kweqiniso kuwo wonke amanani okungenzeka eziguquguqukayo ayingxenye umsebenzi. Ubunikazi kungenziwa imelelwa ukulingana ngezinhlamvu noma ezinombolo.

Ncamashí elilingana aveza eziqukethe zombili izinhlangothi variable ezingaziwa, okungase kufanisa izingxenye ezimbili linye.

Uma sithola esikhundleni esisodwa Inkulumo ngomunye, okuyinto ilingana, uma kuziwa ungubani ukuguqulwa. Kulokhu, ungasebenzisa amafomula zokuphindaphinda ezifingqiwe, imithetho izibalo kanye nezinye ubunikazi.

Ukuze wehlise ingxenyenamba, kubalulekile ukuba afeze ungubani kugucuka. Ngokwesibonelo, ingxenyenamba inikezwe. Ukuze uthole imiphumela, kufanele usebenzise amafomula of ezifingqiwe ukubuyabuyelela, factorization, yokuncishiswa nokwehlisa Inkulumo kwamafrakshini.

It kuyafaneleka ukucabangela le nkulumo izoba ezifanayo lapho zihilela akulingani 3.

5 izindlela ukufakazela ungubani

Ukuze afakazele ukuthi ungubani, udinga ukuba afeze ekuguquleni indlela yokuzikhombisa.

mina indlela

Kuyadingeka ukuba ukuqhuba esibalelwa ukuguqula ohlangothini lwesobunxele. Umphumela uba ngakwesokunene, singasho ukuthi ungubani kubonakaliswa.

II indlela

Zonke izenzo ukuguqulwa yokukhuluma zenzeka esandleni sokudla. Waba yini umphumela wesibindi manipulation luluhlangothi sobunxele. Uma zombili izingxenye ayafana, ubunikazi kubonakaliswa.

III indlela

"Inguquko" zenzeka yomibili le nkulumo. Uma ngenxa yalokho sithola izingxenye ezimbili ezifanayo, ungubani kubonakaliswa.

IV indlela

Kusukela ohlangothini lwesobunxele ohlangothini olusesandleni sokunene is sisuswe. Ngenxa kugucuka okulingana kufanele uthole zero. Khona-ke sikwazi ukukhuluma ubunikazi yokukhuluma.

V indlela

Ingabe sisuswe ohlangothini lwesokunene ngakwesobunxele. Zonke esibalelwa uguqule enciphile yokuthi impendulo kwaba zero. kulokhu kuphela singakhuluma ukuthi ingubani ukulingana.

I izakhiwo eziyisisekelo ubunikazi

Esifundweni sezibalo zibalo izakhiwo avame ukusetshenziswa ukuze kusheshiswe umsebenzi kathisha. Ngenxa inqubo eziyisisekelo kubalwa i ubunikazi algebraic amagama athile kuthatha imizuzu kunalokho amahora amade.

• X + Y = Y + X
• X + (Y + C) = (X + Y) + C
• + X 0 = X
• X + (-X) = 0
• X ∙ (Y + C) = 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, lapho X ≠ 0

Amafomula zokuphindaphinda ezifingqiwe

Ngezinye ifomula ewumgogodla kuthiwa ezifingqiwe ukubuyabuyelela zibalo. Asiza ukuxazulula izinkinga eziningi izibalo ngenxa alula futhi lula ukusetshenziswa.

• (A + B) ² = A ² + 2 ∙ ∙ B + B ² - sikwele isamba pair of izinombolo;

• (A - B) ² = A ² - A 2 ∙ ∙ B + B ² - i-pair of yisikwele umehluko izinombolo;

• (C + B) ∙ (C - C) = C ² - B ² - umehluko tikwele;

• (A + B) = ³ + 3 ^{3 2} ∙ ∙ Ngo + 3 ∙ A ∙ B ² + B ³ - cube lemali;

• (A - B) ³ = A ³ - A ² 3 ∙ ∙ B + A 3 ∙ ∙ V ² - V ³ - umehluko cubic;

• (P + B) ∙ (P ² - P ∙ B + B ²⁾ = F ³ IN ³ + - isamba cubes;

• (P - B) ∙ (P ² + P ∙ B + B ²⁾ = P ³ - B ³ - umehluko cubes.

Ezifingqiwe ukubuyabuyelela ifomula ngokuvamile sisetshenziswa uma ufuna ukuba ahole polynomial efomini evamile ngokuzenza zibe lula kuwo wonke izindlela kungenzeka. Emelelwa ifomula obubonisa, vele uvule amabhrakhethi futhi kuholele imigomo efanayo.

kwesibalo

Ngemva kokutadisha umbuzo, yini ndaba, ungakwazi uqhubekele esinyathelweni esilandelayo: uyini equation. Ngaphansi kwesibalo waqonda ukulingana, lapho amanani engaziwa khona. Isixazululo of the equation ubizwa ngokuthi ukuthola zonke amagugu kwenombolo lapho izingxenye ezimbili lonke Inkulumo kuzolingana. Futhi, kukhona imisebenzi lapho akunakwenzeka ukuthola izixazululo of the equation. Kulokhu sithi ukuthi azikho izimpande.

Njengomthetho, ukulingana engaziwa njengoba isixazululo ukunikeza integers. Nokho, zikhona izimo lapho izimpande Vector imisebenzi, kanye nezinye izinto.

I kwesibalo ingenye imiqondo ebaluleke kakhulu kwi-mathematics. Izinkinga eziningi yesayensi ezingokoqobo musa ukukala noma ukubala noma iliphi inani. Ngakho-ke, kumele ube isilinganiso okuzokwenza ukwanelisa zonke nemibandela umsebenzi. Ngo inqubo lokhu isilinganiso livela kwesibalo noma isimiso zibalo.

Ngokuvamile ikhambi ukulingana ne engaziwa kunciphisa ekutjhugulukeni ezothando eziyinkimbinkimbi, futhi yawanciphisa kumumo elula. Kumele kukhunjulwe ukuthi ukuguqulwa kumele kwenziwe mayelana yomibili, kungenjalo okukhiphayo uzoguqula yi okungalungile.

4, indlela yokuxazulula ezothando

Ngu isixazululo of the equation unikezwa ukuqonda isikhundla solunye ukuthi okulingana ngowokuqala. Lesi senzo njengoba ungubani ukuguqulwa ezaziwayo. Ukuze kuxazululwe le equation, kufanele usebenzise eyodwa yezindlela.

1. Omunye Inkulumo esikhundleni ngomunye, okuyinto ngempela kuyoba liyefana yini kuqala. Isibonelo: (3 ∙ x + 3) ² = 15 + 10 x ∙. Le nkulumo ingase ukuguqulelwa 9 ∙ x ² + 18 x ∙ = 15 + 9 + 10 x ∙.

2. Ukudluliselwa amalungu ilingane engaziwa kusuka kolunye uhlangothi kuya kolunye. Kulokhu-ke kuyadingeka ukushintsha izimpawu ngendlela efanele. I kancane iphutha incithakalo yonke mayelana nomsebenzi owenziwayo. Njengoba isibonelo, ukuthatha "isampula" odlule.

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

Khona-ke ezothando isixazululekile usebenzisa discriminant.

3. Phindaphinda zombili izinhlangothi elilinganayo noma isisho akulingani 0. Nokho, kuwufanele ukukhumbula ukuthi lapho equation omusha ayilingani kuya nokulingana ngaphambi ushintsho, bese inani izimpande ziyahlukahluka kakhulu.

4. Squaring zombili izinhlangothi equation. Le ndlela kumane emangalisayo, ikakhulukazi uma ukulingana uwukubonakaliswa engenangqondo okungukuthi, impande skwele inkulumo ethi ngaphansi kwaso. Kukhona eyodwa caveat: uma ukwakha kwesibalo e ngisho degree ke kungase kubonakale izimpande nezingahlobene nendaba, okuyinto phendulela okushiwo umsebenzi. Futhi uma akulungile ukuthatha impande ke okushiwo umbuzo kule nkinga alucacile. ISIBONELO: │7 ∙ h│ = 35 → 1) 7 ∙ x = 35 no-2) - 7 ∙ x = 35 → kwesibalo ziyoxazululwa kahle.

Ngakho, lesi sihloko imayelana imigomo ezifana zibalo nobunikazi. Konke kuye kwaba khona kuvela "ukulingana" umqondo. Ngenxa tinhlobo letehlukene izibalo ezilingene ukuze ikhambi izinkinga ezithile ngokwezinga elikhulu lula.