Indlela ukuxazulula kwesibalo komugqa ngokusebenzisa amaphuzu amabili?

Mathematics - isayensi akuyona boring njengoba kubonakala ngezinye izikhathi. It has a lot of ezithakazelisayo, nakuba ngezinye izikhathi engaqondakali kulabo akakuthandi lokuba siliqonde. Namuhla sizokhuluma omunye eqinisweni ezivamile futhi elula kwi-mathematics, kodwa kunalokho ensimini yayo ukuthi on the esengozini algebra futhi geometry. Ake sixoxe oqondile nezibalo. Kunengqondo ukuthi isikole kuncike isidina, okungadingi azimhambeli ezithakazelisayo futhi ezintsha. Nokho, lokhu akunjalo, futhi lesi sihloko sizozama bakubonise umbono wethu. Ngaphambi kokuya ezithakazelisa kakhulu futhi uchaze equation of umugqa ngokusebenzisa amaphuzu amabili, sibheka umlando wawo onke la izilinganiso, bese uthole ukuthi kungani konke lokhu kwakudingekile futhi kungani manje akusho ubuhlungu ukwazi amafomula elandelayo.

indaba

Ngisho izibalo lasendulo uyakuthanda ezakhiwe Jomethri futhi zonke izinhlobo amagrafu. Kunzima ukusho namuhla, owaqala waqamba kwesibalo komugqa ngokusebenzisa amaphuzu amabili. Kodwa kuthathwa ngokuthi lo muntu kwaba Euclid - usosayensi ngesiGreki sefilosofi. Nguye e indatshana yakhe "Inception" abangele abantu ukuba bazenze nsuku ngekusasa Euclidean geometry. Manje lokhu legatsha wezibalo ubhekwa ngesisekelo ukumelwa weJiyomethri zezwe futhi siyafundwa esikoleni. Kodwa kuwufanele ethi geometry Euclidean isebenza kuphela ezingeni Macro sikalo zethu ezintathu-ntathu. Uma sicabangela isikhala, akusiyo njalo kungenzeka ukuba ukucabanga uyisebenzisa yonke izenzakalo ezenzeka lapho.

Ngemva Euclid nezinye ososayensi. Futhi zakha futhi conceptualized yini wathola nalabhalwako. Ekugcineni, kwacaca ukuthi insimu okusimeme geometry, lapho konke namanje uhlala nesingazanyazanyiswa. Futhi izinkulungwane zeminyaka kwaba ukuthi kwesibalo komugqa ngokusebenzisa amaphuzu amabili ukwenza ilula kakhulu futhi kulula. Kodwa ngaphambi kokuqhubeka incazelo kanjani lokhu, sizoxoxa ngeminye theory.

ithiyori

Direct - i elula engapheli zombili izinkomba, okungase kube izingxenye zibe isibalo esingapheliyo izingxenye anoma yibuphi ubude. Ukuze yethule emgceni locondzile, ihluzo avame ukusetshenziswa. Ngaphezu kwalokho, amagrafu kungaba kokubili mgudumbili futhi ngakuthathu Ukudidiyela uhlelo. Zisekelwe izixhumanisi amaphuzu, zingezohlobo. Phela, uma sicabanga emgceni locondzile, singabona ukuthi siqukethe i isibalo esingapheliyo amaphuzu.

Nokho, kukhona into okungamelwe ngqo wehlukile nezinye izinhlobo imigqa. Lena kwesibalo wakhe. Nakubukwa jikelele, silula, ngokungafani, uthi, ezothando mbuthano. Ngokuqinisekile, ngamunye kithi wathatha-ke esikoleni esiphakeme. Kodwa namanje uwubhala ifomu jikelele: y = Kx + b. Esigabeni esilandelayo kwethulwa siyobonana kahle ukuthi lezi zincwadi nokuthi ukubhekana nalokhu kwesibalo ayinzima komugqa edabula amaphuzu amabili.

I kwesibalo ka umugqa oqondile

I ukulingana ukuthi seyenziwe ngenhla, futhi kubalulekile ukuba asiqondise kuya equation. Kufanele ucacise lapha lisho. Njengoba kungenziwa ukuyichaza, y futhi x - izixhumanisi iphuzu ngalinye okuqondene umugqa. Ngokuvamile, ndaba kuyindlela lapho kuphela ngoba zonke iphuzu noma iyiphi umugqa avame ukuba ngokuhlanganyela nezinye amaphuzu, ngakho kukhona umthetho ngokuxhumanisa eyodwa Ukudidiyela kwenye. Lo mthetho ichaza indlela abukeka ngayo equation of umugqa oqondile ngokusebenzisa amaphuzu amabili esinikeziwe.

Kungani amaphuzu amabili? Konke lokhu ngoba inombolo okungenani amaphuzu adingekayo ukuze kwakhiwe umugqa oqondile e Ubukhulu ezimbili ezimbili. Uma sithatha isikhala ezintathu-ntathu, inani lamaphuzu adingekayo ukuze kwakhiwe umugqa owodwa ngqo beyoba elilingana ezimbili, njengoba amaphuzu amathathu kakade bakha indiza.

Kukhona theorem, efakazela ukuthi ngokusebenzisa amaphuzu amabili kungenzeka ukwenza umugqa owodwa ngqo. Leli qiniso angaqinisekiswa practice, yokuxhuma umugqa amaphuzu amabili okungahleliwe kugrafu.

Manje ake sihlole isibonelo esikhethekile futhi ubonise kanjani ukubhekana nale kwesibalo elibi umugqa edabula amaphuzu amabili esinikeziwe.

Ngokwesibonelo

Cabangela amaphuzu amabili, lapho udinga ukwakha umugqa. Sichaza isikhundla sabo, isibonelo, M ₁ (2 1) no-M ₂ (3; 2). Njengoba sazi kusukela sesikole, owokuqala Ukudidiyela - ukubaluleka the OX-eksisi, kanti eyesibili - ku-eksisi Oy. Lokhu okungenhla sekube ezothando eqondile matemu amabili, futhi esingawafunda nemingcele ulahlekile k futhi b, udinga ukusetha i-system of zibalo ezimbili. Eqinisweni, kuyothiwa sakhiwa zibalo ezimbili, ngayinye okuzoba constants zethu ezimbili engaziwa:

1 = 2k + b

2 = 3k + b

Manje uhlala into ebaluleke kakhulu: ukuxazulula lesi simiso. Lokhu kwenziwa impela nje. Ukuze liveze ekuqaleni kwesibalo b lokuqala: b = 1-2k. Manje thina kudingeke bamelele ezothando okuholela phakathi kwesibalo yesibili. Lokhu kwenziwa ngokufaka esikhundleni b yithi okuholela kwesibalo:

2 = 3k + 1-2k

1 = k;

Manje njengoba sazi ukuthi yikuphi ukubaluleka k Coefficient, kusho ukuthi sekuyisikhathi sokuba bafunde ukubaluleka okulandelayo njalo - b. Kuba lula ngisho. Njengoba sazi ukwencika b ku k, singakwazi bamelele ukubaluleka the yokugcina kule ndaba okokuqala futhi uthole inani elingaziwa:

b = 1-2 * 1 = -1.

Ukwazi kokubili okuza, manje singaba bamelele kubo kule ndaba yokuqala jikelele emgqeni ngokusebenzisa amaphuzu amabili. Ngakho, ngokwesibonelo yethu, sithola ezothando elandelayo: y = x-1. Lona ukulingana oyifunayo, okuyinto kufanele sibhale uthole.

Ngaphambi sifinyelele isiphetho, sixoxa isicelo yaleli gatsha wezibalo ekuphileni kwansuku zonke.

isicelo

Ngenxa yalokho, isicelo of the equation of umugqa oqondile ngokusebenzisa amaphuzu amabili akuyona. Kodwa lokhu akusho ukuthi asikho isidingo kithi. Ngo-physics kanye mathematics kakhulu ngenkuthalo esetshenziswa zibalo imigca kanye izakhiwo ezidalwa yilokhu. Ungase angaluboni, kodwa izibalo elisizungezile. Ngisho izifundo ezibonakala zingezona ezibonakalayo ezifana kwesibalo komugqa ngokusebenzisa amaphuzu amabili ongazithola ziwusizo kakhulu futhi ngokuvamile kakhulu isicelo ezingeni eliyisisekelo. Uma efika kuqala kubonakala sengathi lokhu ndawo kungaba wusizo, khona-ke kukhona okungalungile. Mathematics eba ukucabanga okunengqondo, okuyinto akasoze abe phezu.

isiphetho

Manje, uma senza esiphethweni indlela yokwakha oqondile amaphuzu amabili idatha, sicabanga lutho ukuphendula noma yimuphi umbuzo ezihlobene nale. Isibonelo, uma uthisha uthi kuwe, "Bhala equation of umugqa edabula amaphuzu amabili", ngakho-ke angeke kube nzima ukwenza kanjalo. Sithemba ukuthi kulesi sihloko esiye sanezela kuwusizo kuwe.