Whakaoti i te x^2-10x+24

$$x ^ { 2 } - 10 x + 24$$

Tauwehe

$$\left(x-6\right)\left(x-4\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx+24. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-10 ab=1\times 24=24$$

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 24.

$$-1,-24 -2,-12 -3,-8 -4,-6$$

Tātaihia te tapeke mō ia takirua.

$$-1-24=-25 -2-12=-14 -3-8=-11 -4-6=-10$$

Ko te otinga te takirua ka hoatu i te tapeke -10.

$$a=-6 b=-4$$

Tuhia anō te x^{2}-10x+24 hei \left(x^{2}-6x\right)+\left(-4x+24\right).

$$\left(x^{2}-6x\right)+\left(-4x+24\right)$$

Tauwehea te x i te tuatahi me te -4 i te rōpū tuarua.

$$x\left(x-6\right)-4\left(x-6\right)$$

Whakatauwehea atu te kīanga pātahi x-6 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-6\right)\left(x-4\right)$$

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.

$$x^{2}-10x+24=0$$

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.

$$x=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}-4\times 24}}{2}$$

Pūrua -10.

$$x=\frac{-\left(-10\right)±\sqrt{100-4\times 24}}{2}$$

Whakareatia -4 ki te 24.

$$x=\frac{-\left(-10\right)±\sqrt{100-96}}{2}$$

Tāpiri 100 ki te -96.

$$x=\frac{-\left(-10\right)±\sqrt{4}}{2}$$

Tuhia te pūtakerua o te 4.

$$x=\frac{-\left(-10\right)±2}{2}$$

Ko te tauaro o -10 ko 10.

$$x=\frac{10±2}{2}$$

Nā, me whakaoti te whārite x=\frac{10±2}{2} ina he tāpiri te ±. Tāpiri 10 ki te 2.

$$x=\frac{12}{2}$$

Whakawehe 12 ki te 2.

$$x=6$$

Nā, me whakaoti te whārite x=\frac{10±2}{2} ina he tango te ±. Tango 2 mai i 10.

$$x=\frac{8}{2}$$

Whakawehe 8 ki te 2.

$$x=4$$

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 6 mō te x_{1} me te 4 mō te x_{2}.

$$x^{2}-10x+24=\left(x-6\right)\left(x-4\right)$$

Aromātai

$$\left(x-6\right)\left(x-4\right)$$