Whakaoti i te x^2+x-342=

$$x ^ { 2 } + x - 342 =$$

Tauwehe

$$\left(x-18\right)\left(x+19\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx-342. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=1 ab=1\left(-342\right)=-342$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -342.

$$-1,342 -2,171 -3,114 -6,57 -9,38 -18,19$$

Tātaihia te tapeke mō ia takirua.

$$-1+342=341 -2+171=169 -3+114=111 -6+57=51 -9+38=29 -18+19=1$$

Ko te otinga te takirua ka hoatu i te tapeke 1.

$$a=-18 b=19$$

Tuhia anō te x^{2}+x-342 hei \left(x^{2}-18x\right)+\left(19x-342\right).

$$\left(x^{2}-18x\right)+\left(19x-342\right)$$

Tauwehea te x i te tuatahi me te 19 i te rōpū tuarua.

$$x\left(x-18\right)+19\left(x-18\right)$$

Whakatauwehea atu te kīanga pātahi x-18 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-18\right)\left(x+19\right)$$

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.

$$x^{2}+x-342=0$$

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.

$$x=\frac{-1±\sqrt{1^{2}-4\left(-342\right)}}{2}$$

Pūrua 1.

$$x=\frac{-1±\sqrt{1-4\left(-342\right)}}{2}$$

Whakareatia -4 ki te -342.

$$x=\frac{-1±\sqrt{1+1368}}{2}$$

Tāpiri 1 ki te 1368.

$$x=\frac{-1±\sqrt{1369}}{2}$$

Tuhia te pūtakerua o te 1369.

$$x=\frac{-1±37}{2}$$

Nā, me whakaoti te whārite x=\frac{-1±37}{2} ina he tāpiri te ±. Tāpiri -1 ki te 37.

$$x=\frac{36}{2}$$

Whakawehe 36 ki te 2.

$$x=18$$

Nā, me whakaoti te whārite x=\frac{-1±37}{2} ina he tango te ±. Tango 37 mai i -1.

$$x=-\frac{38}{2}$$

Whakawehe -38 ki te 2.

$$x=-19$$

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 18 mō te x_{1} me te -19 mō te x_{2}.

$$x^{2}+x-342=\left(x-18\right)\left(x-\left(-19\right)\right)$$

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

$$x^{2}+x-342=\left(x-18\right)\left(x+19\right)$$

Aromātai

$$\left(x-18\right)\left(x+19\right)$$