Whakaoti i te k^2-2k-35

$$k ^ { 2 } - 2 k - 35$$

Tauwehe

$$\left(k-7\right)\left(k+5\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei k^{2}+ak+bk-35. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-2 ab=1\left(-35\right)=-35$$

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 -35.

$$1,-35 5,-7$$

Tātaihia te tapeke mō ia takirua.

$$1-35=-34 5-7=-2$$

Ko te otinga te takirua ka hoatu i te tapeke -2.

$$a=-7 b=5$$

Tuhia anō te k^{2}-2k-35 hei \left(k^{2}-7k\right)+\left(5k-35\right).

$$\left(k^{2}-7k\right)+\left(5k-35\right)$$

Tauwehea te k i te tuatahi me te 5 i te rōpū tuarua.

$$k\left(k-7\right)+5\left(k-7\right)$$

Whakatauwehea atu te kīanga pātahi k-7 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(k-7\right)\left(k+5\right)$$

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.

$$k^{2}-2k-35=0$$

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.

$$k=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-35\right)}}{2}$$

Pūrua -2.

$$k=\frac{-\left(-2\right)±\sqrt{4-4\left(-35\right)}}{2}$$

Whakareatia -4 ki te -35.

$$k=\frac{-\left(-2\right)±\sqrt{4+140}}{2}$$

Tāpiri 4 ki te 140.

$$k=\frac{-\left(-2\right)±\sqrt{144}}{2}$$

Tuhia te pūtakerua o te 144.

$$k=\frac{-\left(-2\right)±12}{2}$$

Ko te tauaro o -2 ko 2.

$$k=\frac{2±12}{2}$$

Nā, me whakaoti te whārite k=\frac{2±12}{2} ina he tāpiri te ±. Tāpiri 2 ki te 12.

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

Whakawehe 14 ki te 2.

$$k=7$$

Nā, me whakaoti te whārite k=\frac{2±12}{2} ina he tango te ±. Tango 12 mai i 2.

$$k=-\frac{10}{2}$$

Whakawehe -10 ki te 2.

$$k=-5$$

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 7 mō te x_{1} me te -5 mō te x_{2}.

$$k^{2}-2k-35=\left(k-7\right)\left(k-\left(-5\right)\right)$$

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

$$k^{2}-2k-35=\left(k-7\right)\left(k+5\right)$$

Aromātai

$$\left(k-7\right)\left(k+5\right)$$