Whakaoti i te h^2+20h+19

$$h ^ { 2 } + 20 h + 19$$

Tauwehe

$$\left(h+1\right)\left(h+19\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei h^{2}+ah+bh+19. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=20 ab=1\times 19=19$$

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. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=1 b=19$$

Tuhia anō te h^{2}+20h+19 hei \left(h^{2}+h\right)+\left(19h+19\right).

$$\left(h^{2}+h\right)+\left(19h+19\right)$$

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

$$h\left(h+1\right)+19\left(h+1\right)$$

Whakatauwehea atu te kīanga pātahi h+1 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(h+1\right)\left(h+19\right)$$

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.

$$h^{2}+20h+19=0$$

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.

$$h=\frac{-20±\sqrt{20^{2}-4\times 19}}{2}$$

Pūrua 20.

$$h=\frac{-20±\sqrt{400-4\times 19}}{2}$$

Whakareatia -4 ki te 19.

$$h=\frac{-20±\sqrt{400-76}}{2}$$

Tāpiri 400 ki te -76.

$$h=\frac{-20±\sqrt{324}}{2}$$

Tuhia te pūtakerua o te 324.

$$h=\frac{-20±18}{2}$$

Nā, me whakaoti te whārite h=\frac{-20±18}{2} ina he tāpiri te ±. Tāpiri -20 ki te 18.

$$h=-\frac{2}{2}$$

Whakawehe -2 ki te 2.

$$h=-1$$

Nā, me whakaoti te whārite h=\frac{-20±18}{2} ina he tango te ±. Tango 18 mai i -20.

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

Whakawehe -38 ki te 2.

$$h=-19$$

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

$$h^{2}+20h+19=\left(h-\left(-1\right)\right)\left(h-\left(-19\right)\right)$$

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

$$h^{2}+20h+19=\left(h+1\right)\left(h+19\right)$$

Aromātai

$$\left(h+1\right)\left(h+19\right)$$