Inani cubes kanye umehluko yabo: emelela Formula ukubuyabuyelela

Mathematics - ungomunye walabo nesayensi kubalulekile ukuba khona abantu. Cishe kuzo zonke izinyathelo, kuzo zonke izinqubo ezihilela ukusetshenziswa wezibalo kanye nokusebenza kwayo okusemqoka. Ososayensi abaningi kakhulu baye benza imizamo okukhulu ukuqinisekisa ukuthi isayensi yokwenza lokhu kulula futhi enembile. theorems abahlukahlukene kanye namafomula Axiom kuzokwenza abafundi ukuthola ulwazi iwazi. Iningi lawo bekhunjulwa kukho konke ukuphila.

Ifomula elula kunazo evumela abafundi nabafundi ukuze ubhekane ngokuphumelelayo nalesi izibonelo omkhulu, amafraktjhini, izinkulumo okunengqondo engenangqondo kukhona amafomula, kuhlanganise ukubuyabuyelela ezifingqiwe:

1. Isamba futhi umehluko cubes :

s ³ - t ³ - umehluko;

k + l ^{3 3} - sum.

2. Isibalo ifomula cube, kanye umehluko phakathi cube:

(F + g) kanye ³ (h - d) ^3;

3. umehluko izigcawu:

z ² - v ^2;

4. Isikwele sum:

(N + m) ² futhi t. D.

Ifomula isamba cubes kuyinto cishe nzima kakhulu ngekhanda futhi udlale. Lokhu kubangelwa izimpawu kushintshana e emagama ayo. Zibhale ngokungalungile, wayephambanisa kwamanye amafomula.

Isamba cubes livezwe kanje:

³ k + l ³ = (k + l) * (k ² - k * l + l ^2).

Ingxenye yesibili ezothando okungukuthi ngezinye izikhathi kudidaniswe a quadratic equation noma isisho kudalulwe inani isikwele yengezwe yesibili elithi, okuwukuthi, ukuphinde «k * l» inombolo 2. Nokho, ifomula inani cubes wembula kuphela indlela. Masibe ukulingana ka ohlangothini sokunene nesobunxele.

Woza ukuhlanekezela, ngamanye amazwi, ezama ingxenye yesibili (k + l) * (k ² - k * l + l ²⁾ kuyoba ilingane k inkulumo + l ^{3 3.}

Thina ukususa abakaki, siphindaphindeka imigomo. Ukuze wenze lokhu, kuqala uphindaphinde «k» ilunga Inkulumo yesibili ngamunye:

k * (k ² - k * l + k ²⁾ = k * l ² - k * (k * l) + k * (l ^2);

ke ngendlela efanayo umkhiqizo senzo ongaziwa «l»:

l * (k ² - k * l + k ²⁾ = l * k ² - l * (k * l) + l * (l ^2);

lula kwaphumela ukubonakaliswa ifomula inani cubes, kwembule besokunxele, futhi ngesikhathi esifanayo Sinike efanayo imigomo:

(K ³ - k ² * l + k * l ²⁾ + (l * k ² - l ² * k + l ³ ) = K ³ - k ² l + kl ^{2 2} + lk - lk ² + l ³ = k ³ - k ² l + k ² l + kl ² - kl ² + l ³ = k ³ + l ^3.

Le nkulumo ilingana inguqulo yasekuqaleni lemali formula cubes, futhi kufanele uboniswe.

Sithola ubufakazi yokuveza s ³ - t ^3. Lokhu ifomula zezibalo zokuphindaphinda ezifingqiwe libizwa umehluko cubes. it phendla kanje:

s ³ - t ³ = (ama - t) * (s ² + t * s + t ^2).

Ngokufanayo njengoba esikhathini esidlule ukufakazela ngendlela afanayo ilungelo nezingxenye kwesokunxele. Ukuze wenze lokhu, ususe abakaki, siphindaphindeka imigomo:

i engaziwa «s»:

s * (s ² + s * t + t ²⁾ = (s ² + s ³ t + st ^2);

i engaziwa «t»:

t * (s ² + s * t + t ²⁾ = (s ² t + st ² + t ^3);

ukuguqulwa kanye kubakaki ukudalula lo mehluko is etholwe:

s ³ + s ^{2 2} t + st - s ² t - t ³ = s ³ + s ² t- s ² t - - st + st ^{2 2} - t ³ = s ³ - t ³ - njengoba kudingeka ² t s ukufakazela.

Ukuze akhumbule ukuthi izinhlamvu abekelwa zona ukunwetshwa le nkulumo, kubalulekile ukuba sinake izimpawu phakathi imigomo. Ngakho, uma umuntu ongaziwa ahlukaniswa kwenye uphawu zezibalo "-", bese kubhrakhethi lokuqala kuyoba negative, kanti eyesibili - ezimbili plus. Uma etholakala phakathi cubes uphawu "+" Khona-ke, ngokufanayo, a Okuphindaphinda lokuqala yakhiwe plus futhi lokususa yesibili bese plus.

Lokhu kungenziwa amelwe ngesimo izikimu ezincane:

s ³ - t ³ → ( «lokususa") * ( "plus" "plus");

k + l ^{3 3} → ( "plus") * ( "lokususa" "plus").

Cabanga ngalesi sibonelo:

Banikezwe isisho (w - 2) + ³ 8. Kufanele uvule kubakaki.

isixazululo:

(W - 2) + ³ 8 kungenziwa emelelwa (w - 2) + ³ 2 ³

Ngakho, njengoba isamba cubes, le nkulumo ingasho ukunwetshwa ngokuvumelana ifomula zokuphindaphinda ezifingqiwe:

(W - 2 + 2) * ((w - 2) ² - 2 * (w - ²⁾ 2 + ^2);

Khona-ke lula ngokuthi:

w * (w ² - 4w + 4 - 2w + 4 + 4) = w * (w ² - 6w + 12) = w ³ - 6w ² + 12w.

Kulokhu, ingxenye enkulu yokuqala (w - 2) ³ Ungakwazi futhi abhekwe njengendoda umehluko cube:

(H - d) = h ^{3 3} - 3 * h ² * d + 3 * h * d ² - d ^3.

Khona-ke, uma uvula it kule formula, uthola:

(W - 2) ³ = w ³ - 3 * w ² * ² + 3 * ² * w ² - 2 ³ = w ³ - 6 * w ² + 12w - 8.

Uma sinezela ke ingxenye izibonelo yasekuqaleni yesibili, ethi "8", umphumela simiswe ngalendlela lelandzelako:

(W - 2) + 8 ³ = w ³ - 3 * w ² * ² + 3 * ² * w ² - 2 ³ + 8 = w ³ - 6 * w ² + 12w.

Ngakho, sithole isixazululo sale Ngokwesibonelo ngezindlela ezimbili.

Kumele kukhunjulwe ukuthi isihluthulelo sempumelelo kunoma yiliphi ibhizinisi, kuhlanganise ekuxazululeni izibonelo zezibalo kukhona ukuphikelela nokunakekela.