Yintoni ukulingana? Uphawu lokuqala imigaqo ukulingana kunye

"Ukulingana" - nesihloko abafundi usesesikolweni aphantsi. It iya abe "ukungalingani 'yakhe. La magama mabini zihlobene. Ngaphezu koko, nabo ezinxulumene amagama afana equation yesazisi. Ngoko ke yintoni na ukulingana?

Ingcamango ukulingana

Xa eli gama ekuthethwa iingxelo kwingxelo ukuba kukho umqondiso "=". Ukulingana zahlulwe zibe okulungileyo nokubi. Ukuba ukurekhodwa ixabisa endaweni = <,>, xa kufikwa nokungalingani. Hi ndlela leyi, lowokuqala umqondiso yokulingana ithi ukuba iinxalenye ezimbini binzana afanayo enziwa japan yayo okanye ingxelo.

Ukongeza ingqiqo yokulingana, isikolo nayo yafunda isihloko "ukulingana wokwamanani". Phantsi kwale ngxelo ukuqonda amabinzana amabini yamanani ezima ngapha nangapha = uphawu. Umzekelo, 2 * 5 + 7 = 17. Zombini isithuba iyalingana.

Xa zisephezulu olu hlobo zingasetyenziswa kwizibiyeli echaphazela nkqubo. Ngoko ke, kukho imithetho-4 ekufuneka ithathelwe ingqalelo xa kubalwa iziphumo amabinzana ngamanani.

1. Ukuba entry akukho parentheses, ngoxa imisebenzi lwenziwa ukusuka linyathelo ephakamileyo: III → II → I. Ukuba kukho amanyathelo aliqela udidi enye, ngoko ke ukusuka ekhohlo ukuya ekunene.
2. Ukuba ngerekhodi braces, ngoko ke inyathelo lwenziwa kwindawo yegama, uze kuthathelwa ingqalelo amanyathelo. Mhlawumbi kwizibiyeli ziya kuba ngaphezulu.
3. Ukuba ibinzana umelwe njengeqhezu, ngoko kufuneka uqale ukubala inani elingezantsi, ngoko elingezantsi, ngoko elingezantsi bahlulwe elingezantsi.
4. Ukuba lamarekhodi yegama ekwiseli, ngoko ke ibinzana lokuqala ivavanywa kwizibiyeli embilwini.

Ngoko ke, ngoku ke kucacile ukuba ukulingana ezinjalo. Kwixesha elizayo, isigama kuya kuxoxwa lenxaki, ubuni bakho kunye neendlela ukubala kwabo.

Properties zibalo zisephezulu

Yintoni ukulingana? Uphononongo kolu luvo kufuna ulwazi iimpawu zengqwalaselo ngamanani. Le fomyula umbhalo zilandelayo ukuvumela ukuba siqonde ngcono le sihloko. Kakade ke, le mihlaba zifaneleke ngakumbi ngenxa isifundo kwemathematika kwisikolo samabanga aphakamileyo.

1. Le ukulingana wokwamanani akayi iyolala ukuba iinxalenye zayo zombini dibanisa inani elifanayo ukuba ibinzana okhoyo.

A ↔ B = A + B = 5 + 5

2. Musa iyolala lenxaki, ukuba omabini amacala nanda okanye lahlulwe ngenani elifanayo okanye intetho, ezahlukileyo zero.

↔ P = O P = O ∙ 5 ∙ 5

P = O ↔ R 5 = Malunga ne-5

3. Ukongeza omabini amacala ungubani umsebenzi ofanayo, eyenza ingqiqo kuwo onke amaxabiso eli variable, sinokuyifumana quadratic entsha, leyo kulingana ngexabiso yokuqala.

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

4. Nayiphi gama okanye binzana kutshintshelwa kwelinye icala lophawu ngokulinganayo, kuya kufuneka utshintshe umqondiso.

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

5. phinda okanye yahlula macala ngo 'umsebenzi ofanayo ukuba wahlukile ukusuka kwiqanda nokuba intsingiselo ukwenzela ixabiso ngalinye X evela DHS, sinokuyifumana quadratic entsha, leyo kulingana ngexabiso yokuqala.

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 migaqo abonisa ngokucacileyo ngesidanga yomgaqo wolingano, oluba phantsi kweemeko ezithile.

Ingcamango zinkulu

Kwimathematika kukho ikho into ukulingana yonxulumano. Kule meko kuthetha ekumiseleni enkulu. Ukuba icandelo A B, ngoko umphumo lulwahlulo inani A ku B. olinganise wabhekisela ukulingana yonxulumano ezimbini:

Maxa wambi kuyinciphise, ibhalwe ngolu hlobo lulandelayo: A: B = C: D. yoko olinganise impahla esisiseko: A * D = D * C , apho A no D - ukuzibaxa ibonwe ngaphambili, kunye B no C - medium.

ezichazwa

Identity kuthiwa ukulingana, nto leyo eya kuba njalo kuwo onke amaxabiso kunokwenzeka yezahlukileyo ukuba yinxenye yomsebenzi. Zokuchonga angamelwa nokulingana alphabetic okanye yamanani.

Ukukhetha kulingana na amabinzana eziqulathe omabini amacala variable engaziwa, leyo umyinge iinxalenye ezimbini wonke omnye.

Ukuba sisondela ilalela yebinzana omnye komnye, leyo ilingana, xa kufikwa inguqu isazisi. Kulo mzekelo, ungasebenzisa iifomyula-phindo esishwankathelweyo, imithetho izibalo kunye ezinye ingqwalasela.

Ukunciphisa iqhezu, kuyimfuneko ukwenza zinguquko yesazisi. Umzekelo, a iqhekeza elinikiweyo. Ukuze ufumane iziphumo, kufuneka usebenzise iifomyula-phindo esishwankathelweyo, factorization, lula nokuncitshiswa yokuvakalisa amaqhezu.

Iyafuna ucinga ukuba eli binzana iza kufana twatse xa elingezantsi akalingani-3.

5 iindlela ukuvelisa ubumi

Ukuze ukungqina ukuba ngubani, kufuneka enze inguqu amabinzana.

I indlela

Kuyimfuneko ukuba ukuqhuba kwizi ukuguqula kwicala lasekhohlo. Isiphumo ngasekunene, ibe nathi singatsho ukuba ubungqina ukuba ungubani.

indlela II

Zonke iintshukumo kwi inguqu yokuthetha kwenzeka kwicala lasekunene. Ngesiphumo entamo icala lasekhohlo. Ukuba zombini iindawo ziyafana, ukuzichaza lawo.

indlela III

"Inguqu" kwenzeka zombini iindawo binzana. Ukuba ngenxa sifumana iinxalenye ezimbini ezifanayo, obuchazwe kubonakaliswa.

indlela IV

Ukusuka kwicala lasekhohlo kwicala lasekunene-isandla sisuswe. Ngenxa utshintshwano ezilinganayo kufanele zero. Emva koko ke sithethe malunga ungubani elithi.

V indlela

Ngaba sisuswe kwicala lasekunene ekhohlo. Yonke wenani nokuguqula nokuphungulwa yokuba impendulo yaba zero. Kuphela kule meko singakwazi ukuthetha malunga ungubani ukulingana.

Iimpawu ezisisiseko zengqwalaselo

Kwimathematika zibalo iipropati adla ngokusetyenziswa ukukhawulezisa inkqubo yokusebenzisa ikhompyutha. Ngenxa inkqubo esisiseko ukubala i zengqwalaselo aljibra amabinzana athile kuthatha imizuzu kunokuba iiyure ezinde.

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

Le fomyula-phindo esishwankathelweyo

Xa ifomula yayo engundoqo isishwankathelo sembali zibalo-phindo. Banceda ukusombulula iingxaki ezininzi kwizibalo ngenxa elula wayo kanye lula ukusetyenziswa.

• (A + B) ² = A ² + 2 A ∙ ∙ B + B ² - square isiphumo ipere kwamanani;

• (A - B) ² = A ² - A 2 ∙ ∙ B + B ² - iperi amanani umahluko imbombo-ne;

• (C + B) ∙ (C - C) = C ² - B ² - umahluko izikwere;

• (A + B) = ³ + 3 A ³ A ² ∙ ∙ In + 3 ∙ A ∙ B ² + B ³ - cube imali;

• (A - B) ³ = A ³ - A ² 3 ∙ ∙ B + A 3 ∙ ∙ V ² - V ³ - mahluko cc;

• (P + B) ∙ ^(P-2 - P ∙ B + B ²⁾ = F ^{3 NGO-3} + - sum of the ityhubhu;

• (P - B) ∙ (P ² + P ∙ B + B ²⁾ = P ³ - iityhubhu mahluko - B ^3.

formula phindo esishwankathelweyo isoloko isetyenziswa xa ufuna ukukhokela polynomial kwifomu eqhelekileyo ngokuthi lula kuyo zonke iindlela ezinokubakho. Yandlalwa ungenza wazibonakalisa formula, vele uvule kwizibiyeli kunye nesiphumo efanayo.

equation

Emva kokufunda lo mbuzo, yintoni na inxaki, uyakwazi ukuqhubeka kwinyathelo elilandelayo: yintoni na le nxaki. Phantsi equation uyeva ukulingana, apho izixa ezingaziwayo langoku. Isisombululo lenxaki kuthiwa ukufumana onke amaxabiso kukho mahluko apho iinxalenye ezimbini yonke binzana iya kulingana. Kwakhona, kukho imisebenzi apho akunakwenzeka ukufumana izisombululo zale nxaki. Kule meko sithi akukho iingcambu.

Njengomgaqo, ukulingana engaziwayo njengesisombululo ukunika integers. Nangona kunjalo, kukho iimeko apho iingcambu imisebenzi kumda wesangqa, kunye nezinye izinto.

Inxaki yenye yezi ngongoma ibalulekileyo kwimathematika. Uninzi iingxaki yenzululwazi kunye nezenziwayo musa ukulinganisa okanye ubale naliphi na inani. Ngoko ke, kufuneka ube umlinganiselo eya kwanelisa yonke imiqathango msebenzi. Kwinkqubo yalo ratio kubonakala nxaki okanye inkqubo kwizibalo.

Ngokuqhelekileyo isisombululo ukulingana kunye ongaziwayo kunciphisa kwinguqu quadratic oluntsonkothileyo, kunye nokunciphisa yona imilo elula. Kufuneka kukhunjulwe ukuba ukuguqulwa kufuneka wenziwe ngokuphathelele zombini iindawo, kungenjalo imveliso ndiya kukubuyisa isiphumo engalunganga.

4, indlela ukusombulula inxaki

Ngu isisombululo lenxaki elinikiweyo ukuqonda enye into kulingana ngexabiso kuqala. Loo nto yaziwa ngokuba inguqu yesazisi. Ukusombulula inxaki, kufuneka usebenzise enye indlela.

1. Enye nkulumo indawo lelinye, nto leyo ngokuyimfuneko iza kufana twatse kuqala. Umzekelo: (3 ∙ x + 3) ² = 15 + 10 x ∙. Eli binzana anokuguqulwa abe 9 ∙ x ² + 18 x ∙ = 15 + 9 + 10 x ∙.

2. I-transfer lwamalungu elilingana ongaziwayo ukusuka kwelinye icala ukuya kwelinye. Kule meko kuyimfuneko ukutshintsha imiqondiso ngokuchanekileyo. Ahlangane impazamo umonakalo owenziwe wonke umsebenzi. Ngokomzekelo, thatha i "isampuli" elidlulileyo.

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

Ngoko ke equation iyatyhilwa usebenzisa discriminant.

3. Qhamani kumacala omabini inani elilinganayo okanye ibinzana akalingani 0. Noko ke, kubalulekile ukukhumbula ukuba xa equation omtsha kuyalingana ukulingana phambi kokuba utshintsho, ngoko ke isixa kweengcambu ziyahluka kakhulu.

4. Squaring kumacala omabini alenxaki. Le ndlela nje ephawulekayo, ingakumbi xa ukulingana kubonisa ibubudenge, oko kukuthi, i ingcambu ka'B elithi ngaphantsi kwalo. Kukho omnye caveat: ukuba wakha inxaki e nokuba isidanga, ke ukumzisa abonakale iingcambu esindayo, leyo bayasigqwetha kakuhle umsebenzi. Kwaye ukuba kuphosakele ukuthabatha ingcambu, ngoko ke intsingiselo yalo mbuzo kule ngxaki engacacanga. UMZEKELO: │7 ∙ h│ = 35 → 1) 7 ∙ x = 35 no-2) - 7 ∙ x = 35 → equation ziya kusombululeka ngokuchanekileyo.

Ngoko ke, eli nqaku malunga amagama afana zibalo kunye nobuni. Bonke bavela "ukulingana" le mbono. Ngenxa iintlobo ezahlukeneyo amabinzana ezilinganayo ngesisombululo iingxaki ezithile ubukhulu becala lula.