Whakaoti i te p^2-22p-23

$$p ^ { 2 } - 22 p - 23$$

Tauwehe

$$\left(p-23\right)\left(p+1\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei p^{2}+ap+bp-23. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-22 ab=1\left(-23\right)=-23$$

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. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=-23 b=1$$

Tuhia anō te p^{2}-22p-23 hei \left(p^{2}-23p\right)+\left(p-23\right).

$$\left(p^{2}-23p\right)+\left(p-23\right)$$

Whakatauwehea atu p i te p^{2}-23p.

$$p\left(p-23\right)+p-23$$

Whakatauwehea atu te kīanga pātahi p-23 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(p-23\right)\left(p+1\right)$$

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.

$$p^{2}-22p-23=0$$

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.

$$p=\frac{-\left(-22\right)±\sqrt{\left(-22\right)^{2}-4\left(-23\right)}}{2}$$

Pūrua -22.

$$p=\frac{-\left(-22\right)±\sqrt{484-4\left(-23\right)}}{2}$$

Whakareatia -4 ki te -23.

$$p=\frac{-\left(-22\right)±\sqrt{484+92}}{2}$$

Tāpiri 484 ki te 92.

$$p=\frac{-\left(-22\right)±\sqrt{576}}{2}$$

Tuhia te pūtakerua o te 576.

$$p=\frac{-\left(-22\right)±24}{2}$$

Ko te tauaro o -22 ko 22.

$$p=\frac{22±24}{2}$$

Nā, me whakaoti te whārite p=\frac{22±24}{2} ina he tāpiri te ±. Tāpiri 22 ki te 24.

$$p=\frac{46}{2}$$

Whakawehe 46 ki te 2.

$$p=23$$

Nā, me whakaoti te whārite p=\frac{22±24}{2} ina he tango te ±. Tango 24 mai i 22.

$$p=-\frac{2}{2}$$

Whakawehe -2 ki te 2.

$$p=-1$$

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 23 mō te x_{1} me te -1 mō te x_{2}.

$$p^{2}-22p-23=\left(p-23\right)\left(p-\left(-1\right)\right)$$

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

$$p^{2}-22p-23=\left(p-23\right)\left(p+1\right)$$

Aromātai

$$\left(p-23\right)\left(p+1\right)$$