Whakaoti i te x^2+15x+56

$$x ^ { 2 } + 15 x + 56$$

Tauwehe

$$\left(x+7\right)\left(x+8\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx+56. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=15 ab=1\times 56=56$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōrunga te a+b, he tōrunga hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 56.

$$1,56 2,28 4,14 7,8$$

Tātaihia te tapeke mō ia takirua.

$$1+56=57 2+28=30 4+14=18 7+8=15$$

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

$$a=7 b=8$$

Tuhia anō te x^{2}+15x+56 hei \left(x^{2}+7x\right)+\left(8x+56\right).

$$\left(x^{2}+7x\right)+\left(8x+56\right)$$

Tauwehea te x i te tuatahi me te 8 i te rōpū tuarua.

$$x\left(x+7\right)+8\left(x+7\right)$$

Whakatauwehea atu te kīanga pātahi x+7 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x+7\right)\left(x+8\right)$$

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.

$$x^{2}+15x+56=0$$

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.

$$x=\frac{-15±\sqrt{15^{2}-4\times 56}}{2}$$

Pūrua 15.

$$x=\frac{-15±\sqrt{225-4\times 56}}{2}$$

Whakareatia -4 ki te 56.

$$x=\frac{-15±\sqrt{225-224}}{2}$$

Tāpiri 225 ki te -224.

$$x=\frac{-15±\sqrt{1}}{2}$$

Tuhia te pūtakerua o te 1.

$$x=\frac{-15±1}{2}$$

Nā, me whakaoti te whārite x=\frac{-15±1}{2} ina he tāpiri te ±. Tāpiri -15 ki te 1.

$$x=-\frac{14}{2}$$

Whakawehe -14 ki te 2.

$$x=-7$$

Nā, me whakaoti te whārite x=\frac{-15±1}{2} ina he tango te ±. Tango 1 mai i -15.

$$x=-\frac{16}{2}$$

Whakawehe -16 ki te 2.

$$x=-8$$

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 -8 mō te x_{2}.

$$x^{2}+15x+56=\left(x-\left(-7\right)\right)\left(x-\left(-8\right)\right)$$

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

$$x^{2}+15x+56=\left(x+7\right)\left(x+8\right)$$

Aromātai

$$\left(x+7\right)\left(x+8\right)$$