Whakaoti i te v^2-v-42

$$v ^ { 2 } - v - 42$$

Tauwehe

$$\left(v-7\right)\left(v+6\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei v^{2}+av+bv-42. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-1 ab=1\left(-42\right)=-42$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōraro te a+b, he nui ake te uara pū o te tau tōraro i tō te tōrunga. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -42.

$$1,-42 2,-21 3,-14 6,-7$$

Tātaihia te tapeke mō ia takirua.

$$1-42=-41 2-21=-19 3-14=-11 6-7=-1$$

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

$$a=-7 b=6$$

Tuhia anō te v^{2}-v-42 hei \left(v^{2}-7v\right)+\left(6v-42\right).

$$\left(v^{2}-7v\right)+\left(6v-42\right)$$

Tauwehea te v i te tuatahi me te 6 i te rōpū tuarua.

$$v\left(v-7\right)+6\left(v-7\right)$$

Whakatauwehea atu te kīanga pātahi v-7 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(v-7\right)\left(v+6\right)$$

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.

$$v^{2}-v-42=0$$

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.

$$v=\frac{-\left(-1\right)±\sqrt{1-4\left(-42\right)}}{2}$$

Whakareatia -4 ki te -42.

$$v=\frac{-\left(-1\right)±\sqrt{1+168}}{2}$$

Tāpiri 1 ki te 168.

$$v=\frac{-\left(-1\right)±\sqrt{169}}{2}$$

Tuhia te pūtakerua o te 169.

$$v=\frac{-\left(-1\right)±13}{2}$$

Ko te tauaro o -1 ko 1.

$$v=\frac{1±13}{2}$$

Nā, me whakaoti te whārite v=\frac{1±13}{2} ina he tāpiri te ±. Tāpiri 1 ki te 13.

$$v=\frac{14}{2}$$

Whakawehe 14 ki te 2.

$$v=7$$

Nā, me whakaoti te whārite v=\frac{1±13}{2} ina he tango te ±. Tango 13 mai i 1.

$$v=-\frac{12}{2}$$

Whakawehe -12 ki te 2.

$$v=-6$$

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 -6 mō te x_{2}.

$$v^{2}-v-42=\left(v-7\right)\left(v-\left(-6\right)\right)$$

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

$$v^{2}-v-42=\left(v-7\right)\left(v+6\right)$$

Aromātai

$$\left(v-7\right)\left(v+6\right)$$