Whakaoti i te t^2-17t+70

$$t ^ { 2 } - 17 t + 70$$

Tauwehe

$$\left(t-10\right)\left(t-7\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei t^{2}+at+bt+70. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-17 ab=1\times 70=70$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōraro te a+b, he tōraro hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 70.

$$-1,-70 -2,-35 -5,-14 -7,-10$$

Tātaihia te tapeke mō ia takirua.

$$-1-70=-71 -2-35=-37 -5-14=-19 -7-10=-17$$

Ko te otinga te takirua ka hoatu i te tapeke -17.

$$a=-10 b=-7$$

Tuhia anō te t^{2}-17t+70 hei \left(t^{2}-10t\right)+\left(-7t+70\right).

$$\left(t^{2}-10t\right)+\left(-7t+70\right)$$

Tauwehea te t i te tuatahi me te -7 i te rōpū tuarua.

$$t\left(t-10\right)-7\left(t-10\right)$$

Whakatauwehea atu te kīanga pātahi t-10 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(t-10\right)\left(t-7\right)$$

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.

$$t^{2}-17t+70=0$$

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.

$$t=\frac{-\left(-17\right)±\sqrt{\left(-17\right)^{2}-4\times 70}}{2}$$

Pūrua -17.

$$t=\frac{-\left(-17\right)±\sqrt{289-4\times 70}}{2}$$

Whakareatia -4 ki te 70.

$$t=\frac{-\left(-17\right)±\sqrt{289-280}}{2}$$

Tāpiri 289 ki te -280.

$$t=\frac{-\left(-17\right)±\sqrt{9}}{2}$$

Tuhia te pūtakerua o te 9.

$$t=\frac{-\left(-17\right)±3}{2}$$

Ko te tauaro o -17 ko 17.

$$t=\frac{17±3}{2}$$

Nā, me whakaoti te whārite t=\frac{17±3}{2} ina he tāpiri te ±. Tāpiri 17 ki te 3.

$$t=\frac{20}{2}$$

Whakawehe 20 ki te 2.

$$t=10$$

Nā, me whakaoti te whārite t=\frac{17±3}{2} ina he tango te ±. Tango 3 mai i 17.

$$t=\frac{14}{2}$$

Whakawehe 14 ki te 2.

$$t=7$$

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 10 mō te x_{1} me te 7 mō te x_{2}.

$$t^{2}-17t+70=\left(t-10\right)\left(t-7\right)$$

Aromātai

$$\left(t-10\right)\left(t-7\right)$$