Whakaoti i te w^2-8w-48

$$w ^ { 2 } - 8 w - 48$$

Tauwehe

$$\left(w-12\right)\left(w+4\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei w^{2}+aw+bw-48. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-8 ab=1\left(-48\right)=-48$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōraro te a+b, he nui ake te uara pū o te tau tōraro i tō te tōrunga. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -48.

$$1,-48 2,-24 3,-16 4,-12 6,-8$$

Tātaihia te tapeke mō ia takirua.

$$1-48=-47 2-24=-22 3-16=-13 4-12=-8 6-8=-2$$

Ko te otinga te takirua ka hoatu i te tapeke -8.

$$a=-12 b=4$$

Tuhia anō te w^{2}-8w-48 hei \left(w^{2}-12w\right)+\left(4w-48\right).

$$\left(w^{2}-12w\right)+\left(4w-48\right)$$

Tauwehea te w i te tuatahi me te 4 i te rōpū tuarua.

$$w\left(w-12\right)+4\left(w-12\right)$$

Whakatauwehea atu te kīanga pātahi w-12 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(w-12\right)\left(w+4\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ka taea te huamaha pūrua te tauwehe mā te whakamahi i te huringa ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), ina ko x_{1} me x_{2} ngā otinga o te whārite pūrua ax^{2}+bx+c=0.

$$w^{2}-8w-48=0$$

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$w=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\left(-48\right)}}{2}$$

Pūrua -8.

$$w=\frac{-\left(-8\right)±\sqrt{64-4\left(-48\right)}}{2}$$

Whakareatia -4 ki te -48.

$$w=\frac{-\left(-8\right)±\sqrt{64+192}}{2}$$

Tāpiri 64 ki te 192.

$$w=\frac{-\left(-8\right)±\sqrt{256}}{2}$$

Tuhia te pūtakerua o te 256.

$$w=\frac{-\left(-8\right)±16}{2}$$

Ko te tauaro o -8 ko 8.

$$w=\frac{8±16}{2}$$

Nā, me whakaoti te whārite w=\frac{8±16}{2} ina he tāpiri te ±. Tāpiri 8 ki te 16.

$$w=\frac{24}{2}$$

Whakawehe 24 ki te 2.

$$w=12$$

Nā, me whakaoti te whārite w=\frac{8±16}{2} ina he tango te ±. Tango 16 mai i 8.

$$w=-\frac{8}{2}$$

Whakawehe -8 ki te 2.

$$w=-4$$

Tauwehea te kīanga taketake mā te whakamahi i te ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Me whakakapi te 12 mō te x_{1} me te -4 mō te x_{2}.

$$w^{2}-8w-48=\left(w-12\right)\left(w-\left(-4\right)\right)$$

Whakamāmātia ngā kīanga katoa o te āhua p-\left(-q\right) ki te p+q.

$$w^{2}-8w-48=\left(w-12\right)\left(w+4\right)$$

Aromātai

$$\left(w-12\right)\left(w+4\right)$$