Whakaoti i te d^2-4d-5

$$d ^ { 2 } - 4 d - 5$$

Tauwehe

$$\left(d-5\right)\left(d+1\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei d^{2}+ad+bd-5. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-4 ab=1\left(-5\right)=-5$$

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.

$$a=-5 b=1$$

Tuhia anō te d^{2}-4d-5 hei \left(d^{2}-5d\right)+\left(d-5\right).

$$\left(d^{2}-5d\right)+\left(d-5\right)$$

Whakatauwehea atu d i te d^{2}-5d.

$$d\left(d-5\right)+d-5$$

Whakatauwehea atu te kīanga pātahi d-5 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(d-5\right)\left(d+1\right)$$

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.

$$d^{2}-4d-5=0$$

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.

$$d=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\left(-5\right)}}{2}$$

Pūrua -4.

$$d=\frac{-\left(-4\right)±\sqrt{16-4\left(-5\right)}}{2}$$

Whakareatia -4 ki te -5.

$$d=\frac{-\left(-4\right)±\sqrt{16+20}}{2}$$

Tāpiri 16 ki te 20.

$$d=\frac{-\left(-4\right)±\sqrt{36}}{2}$$

Tuhia te pūtakerua o te 36.

$$d=\frac{-\left(-4\right)±6}{2}$$

Ko te tauaro o -4 ko 4.

$$d=\frac{4±6}{2}$$

Nā, me whakaoti te whārite d=\frac{4±6}{2} ina he tāpiri te ±. Tāpiri 4 ki te 6.

$$d=\frac{10}{2}$$

Whakawehe 10 ki te 2.

$$d=5$$

Nā, me whakaoti te whārite d=\frac{4±6}{2} ina he tango te ±. Tango 6 mai i 4.

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

Whakawehe -2 ki te 2.

$$d=-1$$

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 5 mō te x_{1} me te -1 mō te x_{2}.

$$d^{2}-4d-5=\left(d-5\right)\left(d-\left(-1\right)\right)$$

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

$$d^{2}-4d-5=\left(d-5\right)\left(d+1\right)$$

Aromātai

$$\left(d-5\right)\left(d+1\right)$$