Whakaoti i te 2u^2-34u+60

$$2 u ^ { 2 } - 34 u + 60$$

Tauwehe

$$2\left(u-15\right)\left(u-2\right)$$

Ngā Upane Otinga

Tauwehea te 2.

$$2\left(u^{2}-17u+30\right)$$

Whakaarohia te u^{2}-17u+30. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei u^{2}+au+bu+30. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-17 ab=1\times 30=30$$

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 30.

$$-1,-30 -2,-15 -3,-10 -5,-6$$

Tātaihia te tapeke mō ia takirua.

$$-1-30=-31 -2-15=-17 -3-10=-13 -5-6=-11$$

Ko te otinga te takirua ka hoatu i te tapeke -17.

$$a=-15 b=-2$$

Tuhia anō te u^{2}-17u+30 hei \left(u^{2}-15u\right)+\left(-2u+30\right).

$$\left(u^{2}-15u\right)+\left(-2u+30\right)$$

Tauwehea te u i te tuatahi me te -2 i te rōpū tuarua.

$$u\left(u-15\right)-2\left(u-15\right)$$

Whakatauwehea atu te kīanga pātahi u-15 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(u-15\right)\left(u-2\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$2\left(u-15\right)\left(u-2\right)$$

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.

$$2u^{2}-34u+60=0$$

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.

$$u=\frac{-\left(-34\right)±\sqrt{\left(-34\right)^{2}-4\times 2\times 60}}{2\times 2}$$

Pūrua -34.

$$u=\frac{-\left(-34\right)±\sqrt{1156-4\times 2\times 60}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$u=\frac{-\left(-34\right)±\sqrt{1156-8\times 60}}{2\times 2}$$

Whakareatia -8 ki te 60.

$$u=\frac{-\left(-34\right)±\sqrt{1156-480}}{2\times 2}$$

Tāpiri 1156 ki te -480.

$$u=\frac{-\left(-34\right)±\sqrt{676}}{2\times 2}$$

Tuhia te pūtakerua o te 676.

$$u=\frac{-\left(-34\right)±26}{2\times 2}$$

Ko te tauaro o -34 ko 34.

$$u=\frac{34±26}{2\times 2}$$

Whakareatia 2 ki te 2.

$$u=\frac{34±26}{4}$$

Nā, me whakaoti te whārite u=\frac{34±26}{4} ina he tāpiri te ±. Tāpiri 34 ki te 26.

$$u=\frac{60}{4}$$

Whakawehe 60 ki te 4.

$$u=15$$

Nā, me whakaoti te whārite u=\frac{34±26}{4} ina he tango te ±. Tango 26 mai i 34.

$$u=\frac{8}{4}$$

Whakawehe 8 ki te 4.

$$u=2$$

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 15 mō te x_{1} me te 2 mō te x_{2}.

$$2u^{2}-34u+60=2\left(u-15\right)\left(u-2\right)$$

Aromātai

$$2\left(u-15\right)\left(u-2\right)$$