Whakaoti i te 45s^2-120s+80

$$45 s ^ { 2 } - 120 s + 80$$

Tauwehe

$$5\left(3s-4\right)^{2}$$

Ngā Upane Otinga

Tauwehea te 5.

$$5\left(9s^{2}-24s+16\right)$$

Whakaarohia te 9s^{2}-24s+16. Whakamahia te tikanga tātai pūrua pā, a^{2}-2ab+b^{2}=\left(a-b\right)^{2}, ina a=3s, ina b=4.

$$\left(3s-4\right)^{2}$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$5\left(3s-4\right)^{2}$$

Ngā Upane Whakamahi Tauwehe o te Pūrua Huarua

Ko te tikanga tātai o tēnei huatoru he pūrua huatoru, ka whakareatia pea e tētahi tauwehe pātahi. Ka taea ngā pūrua huatoru te tauwehe mā te kimi i ngā pūtakerua o ngā kīanga tau ārahi, autō hoki.

$$factor(45s^{2}-120s+80)$$

Kimihia te tauwehe pātahi nui rawa o ngā tau whakarea.

$$gcf(45,-120,80)=5$$

Tauwehea te 5.

$$5\left(9s^{2}-24s+16\right)$$

Kimihia te pūtakerua o te kīanga tau ārahi, 9s^{2}.

$$\sqrt{9s^{2}}=3s$$

Kimihia te pūtakerua o te kīanga tau autō, 16.

$$\sqrt{16}=4$$

Ko te pūrua huatoru te pūrua o te huarua ko te tapeke tērā, te huatango rānei o ngā pūtakerua o ngā kīanga tau ārahi, autō hoki, e whakaritea ai te tohu e te tohu o te kīanga tau waenga o te pūrua huatoru.

$$5\left(3s-4\right)^{2}$$

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.

$$45s^{2}-120s+80=0$$

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.

$$s=\frac{-\left(-120\right)±\sqrt{\left(-120\right)^{2}-4\times 45\times 80}}{2\times 45}$$

Pūrua -120.

$$s=\frac{-\left(-120\right)±\sqrt{14400-4\times 45\times 80}}{2\times 45}$$

Whakareatia -4 ki te 45.

$$s=\frac{-\left(-120\right)±\sqrt{14400-180\times 80}}{2\times 45}$$

Whakareatia -180 ki te 80.

$$s=\frac{-\left(-120\right)±\sqrt{14400-14400}}{2\times 45}$$

Tāpiri 14400 ki te -14400.

$$s=\frac{-\left(-120\right)±\sqrt{0}}{2\times 45}$$

Tuhia te pūtakerua o te 0.

$$s=\frac{-\left(-120\right)±0}{2\times 45}$$

Ko te tauaro o -120 ko 120.

$$s=\frac{120±0}{2\times 45}$$

Whakareatia 2 ki te 45.

$$s=\frac{120±0}{90}$$

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 \frac{4}{3} mō te x_{1} me te \frac{4}{3} mō te x_{2}.

$$45s^{2}-120s+80=45\left(s-\frac{4}{3}\right)\left(s-\frac{4}{3}\right)$$

Tango \frac{4}{3} mai i s mā te kimi i te tauraro pātahi me te tango i ngā taurunga, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$45s^{2}-120s+80=45\times \frac{3s-4}{3}\left(s-\frac{4}{3}\right)$$

Tango \frac{4}{3} mai i s mā te kimi i te tauraro pātahi me te tango i ngā taurunga, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$45s^{2}-120s+80=45\times \frac{3s-4}{3}\times \frac{3s-4}{3}$$

Whakareatia \frac{3s-4}{3} ki te \frac{3s-4}{3} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$45s^{2}-120s+80=45\times \frac{\left(3s-4\right)\left(3s-4\right)}{3\times 3}$$

Whakareatia 3 ki te 3.

$$45s^{2}-120s+80=45\times \frac{\left(3s-4\right)\left(3s-4\right)}{9}$$

Whakakorea atu te tauwehe pūnoa nui rawa 9 i roto i te 45 me te 9.

$$45s^{2}-120s+80=5\left(3s-4\right)\left(3s-4\right)$$

Aromātai

$$5\left(3s-4\right)^{2}$$