Whakaoti i te 36+x^2-15x

$$36 + x ^ { 2 } - 15 x$$

Tauwehe

$$\left(x-12\right)\left(x-3\right)$$

Ngā Upane Otinga

Hurinahatia te pūrau ki te āhua tānga ngahuru. Whakaraupapahia ngā kīanga tau mai i te pū teitei rawa ki te mea iti rawa.

$$x^{2}-15x+36$$

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx+36. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-15 ab=1\times 36=36$$

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 36.

$$-1,-36 -2,-18 -3,-12 -4,-9 -6,-6$$

Tātaihia te tapeke mō ia takirua.

$$-1-36=-37 -2-18=-20 -3-12=-15 -4-9=-13 -6-6=-12$$

Ko te otinga te takirua ka hoatu i te tapeke -15.

$$a=-12 b=-3$$

Tuhia anō te x^{2}-15x+36 hei \left(x^{2}-12x\right)+\left(-3x+36\right).

$$\left(x^{2}-12x\right)+\left(-3x+36\right)$$

Tauwehea te x i te tuatahi me te -3 i te rōpū tuarua.

$$x\left(x-12\right)-3\left(x-12\right)$$

Whakatauwehea atu te kīanga pātahi x-12 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-12\right)\left(x-3\right)$$

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.

$$x^{2}-15x+36=0$$

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.

$$x=\frac{-\left(-15\right)±\sqrt{\left(-15\right)^{2}-4\times 36}}{2}$$

Pūrua -15.

$$x=\frac{-\left(-15\right)±\sqrt{225-4\times 36}}{2}$$

Whakareatia -4 ki te 36.

$$x=\frac{-\left(-15\right)±\sqrt{225-144}}{2}$$

Tāpiri 225 ki te -144.

$$x=\frac{-\left(-15\right)±\sqrt{81}}{2}$$

Tuhia te pūtakerua o te 81.

$$x=\frac{-\left(-15\right)±9}{2}$$

Ko te tauaro o -15 ko 15.

$$x=\frac{15±9}{2}$$

Nā, me whakaoti te whārite x=\frac{15±9}{2} ina he tāpiri te ±. Tāpiri 15 ki te 9.

$$x=\frac{24}{2}$$

Whakawehe 24 ki te 2.

$$x=12$$

Nā, me whakaoti te whārite x=\frac{15±9}{2} ina he tango te ±. Tango 9 mai i 15.

$$x=\frac{6}{2}$$

Whakawehe 6 ki te 2.

$$x=3$$

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 12 mō te x_{1} me te 3 mō te x_{2}.

$$x^{2}-15x+36=\left(x-12\right)\left(x-3\right)$$

Aromātai

$$\left(x-12\right)\left(x-3\right)$$