Whakaoti i te x^2-100x+196

$$x ^ { 2 } - 100 x + 196$$

Tauwehe

$$\left(x-98\right)\left(x-2\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx+196. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-100 ab=1\times 196=196$$

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 196.

$$-1,-196 -2,-98 -4,-49 -7,-28 -14,-14$$

Tātaihia te tapeke mō ia takirua.

$$-1-196=-197 -2-98=-100 -4-49=-53 -7-28=-35 -14-14=-28$$

Ko te otinga te takirua ka hoatu i te tapeke -100.

$$a=-98 b=-2$$

Tuhia anō te x^{2}-100x+196 hei \left(x^{2}-98x\right)+\left(-2x+196\right).

$$\left(x^{2}-98x\right)+\left(-2x+196\right)$$

Tauwehea te x i te tuatahi me te -2 i te rōpū tuarua.

$$x\left(x-98\right)-2\left(x-98\right)$$

Whakatauwehea atu te kīanga pātahi x-98 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-98\right)\left(x-2\right)$$

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.

$$x^{2}-100x+196=0$$

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.

$$x=\frac{-\left(-100\right)±\sqrt{\left(-100\right)^{2}-4\times 196}}{2}$$

Pūrua -100.

$$x=\frac{-\left(-100\right)±\sqrt{10000-4\times 196}}{2}$$

Whakareatia -4 ki te 196.

$$x=\frac{-\left(-100\right)±\sqrt{10000-784}}{2}$$

Tāpiri 10000 ki te -784.

$$x=\frac{-\left(-100\right)±\sqrt{9216}}{2}$$

Tuhia te pūtakerua o te 9216.

$$x=\frac{-\left(-100\right)±96}{2}$$

Ko te tauaro o -100 ko 100.

$$x=\frac{100±96}{2}$$

Nā, me whakaoti te whārite x=\frac{100±96}{2} ina he tāpiri te ±. Tāpiri 100 ki te 96.

$$x=\frac{196}{2}$$

Whakawehe 196 ki te 2.

$$x=98$$

Nā, me whakaoti te whārite x=\frac{100±96}{2} ina he tango te ±. Tango 96 mai i 100.

$$x=\frac{4}{2}$$

Whakawehe 4 ki te 2.

$$x=2$$

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 98 mō te x_{1} me te 2 mō te x_{2}.

$$x^{2}-100x+196=\left(x-98\right)\left(x-2\right)$$

Aromātai

$$\left(x-98\right)\left(x-2\right)$$