Whakaoti i te x^2+40x+384

$${ x }^{ 2 } +40x+384$$

Tauwehe

$$\left(x+16\right)\left(x+24\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx+384. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=40 ab=1\times 384=384$$

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 384.

$$1,384 2,192 3,128 4,96 6,64 8,48 12,32 16,24$$

Tātaihia te tapeke mō ia takirua.

$$1+384=385 2+192=194 3+128=131 4+96=100 6+64=70 8+48=56 12+32=44 16+24=40$$

Ko te otinga te takirua ka hoatu i te tapeke 40.

$$a=16 b=24$$

Tuhia anō te x^{2}+40x+384 hei \left(x^{2}+16x\right)+\left(24x+384\right).

$$\left(x^{2}+16x\right)+\left(24x+384\right)$$

Tauwehea te x i te tuatahi me te 24 i te rōpū tuarua.

$$x\left(x+16\right)+24\left(x+16\right)$$

Whakatauwehea atu te kīanga pātahi x+16 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x+16\right)\left(x+24\right)$$

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.

$$x^{2}+40x+384=0$$

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.

$$x=\frac{-40±\sqrt{40^{2}-4\times 384}}{2}$$

Pūrua 40.

$$x=\frac{-40±\sqrt{1600-4\times 384}}{2}$$

Whakareatia -4 ki te 384.

$$x=\frac{-40±\sqrt{1600-1536}}{2}$$

Tāpiri 1600 ki te -1536.

$$x=\frac{-40±\sqrt{64}}{2}$$

Tuhia te pūtakerua o te 64.

$$x=\frac{-40±8}{2}$$

Nā, me whakaoti te whārite x=\frac{-40±8}{2} ina he tāpiri te ±. Tāpiri -40 ki te 8.

$$x=-\frac{32}{2}$$

Whakawehe -32 ki te 2.

$$x=-16$$

Nā, me whakaoti te whārite x=\frac{-40±8}{2} ina he tango te ±. Tango 8 mai i -40.

$$x=-\frac{48}{2}$$

Whakawehe -48 ki te 2.

$$x=-24$$

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 -16 mō te x_{1} me te -24 mō te x_{2}.

$$x^{2}+40x+384=\left(x-\left(-16\right)\right)\left(x-\left(-24\right)\right)$$

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

$$x^{2}+40x+384=\left(x+16\right)\left(x+24\right)$$

Aromātai

$$\left(x+16\right)\left(x+24\right)$$