Whakaoti i te 9+3m=m^2-9/m

$$9 + 3 m = \frac { m ^ { 2 } - 9 } { m }$$

Whakaoti mō m

$$m = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

$$m=-3$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Tē taea kia ōrite te tāupe m ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te m.

$$m\times 9+3mm=m^{2}-9$$

Whakareatia te m ki te m, ka m^{2}.

$$m\times 9+3m^{2}=m^{2}-9$$

Tangohia te m^{2} mai i ngā taha e rua.

$$m\times 9+3m^{2}-m^{2}=-9$$

Pahekotia te 3m^{2} me -m^{2}, ka 2m^{2}.

$$m\times 9+2m^{2}=-9$$

Me tāpiri te 9 ki ngā taha e rua.

$$m\times 9+2m^{2}+9=0$$

Hurinahatia te pūrau ki te āhua tānga ngahuru. Whakaraupapahia ngā kīanga tau mai i te pū teitei rawa ki te mea iti rawa.

$$2m^{2}+9m+9=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei 2m^{2}+am+bm+9. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=9 ab=2\times 9=18$$

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. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 18.

$$1,18 2,9 3,6$$

Tātaihia te tapeke mō ia takirua.

$$1+18=19 2+9=11 3+6=9$$

Ko te otinga te takirua ka hoatu i te tapeke 9.

$$a=3 b=6$$

Tuhia anō te 2m^{2}+9m+9 hei \left(2m^{2}+3m\right)+\left(6m+9\right).

$$\left(2m^{2}+3m\right)+\left(6m+9\right)$$

Tauwehea te m i te tuatahi me te 3 i te rōpū tuarua.

$$m\left(2m+3\right)+3\left(2m+3\right)$$

Whakatauwehea atu te kīanga pātahi 2m+3 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(2m+3\right)\left(m+3\right)$$

Hei kimi otinga whārite, me whakaoti te 2m+3=0 me te m+3=0.

$$m=-\frac{3}{2} m=-3$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe m ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te m.

$$m\times 9+3mm=m^{2}-9$$

Whakareatia te m ki te m, ka m^{2}.

$$m\times 9+3m^{2}=m^{2}-9$$

Tangohia te m^{2} mai i ngā taha e rua.

$$m\times 9+3m^{2}-m^{2}=-9$$

Pahekotia te 3m^{2} me -m^{2}, ka 2m^{2}.

$$m\times 9+2m^{2}=-9$$

Me tāpiri te 9 ki ngā taha e rua.

$$m\times 9+2m^{2}+9=0$$

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.

$$2m^{2}+9m+9=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, 9 mō b, me 9 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{-9±\sqrt{9^{2}-4\times 2\times 9}}{2\times 2}$$

Pūrua 9.

$$m=\frac{-9±\sqrt{81-4\times 2\times 9}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$m=\frac{-9±\sqrt{81-8\times 9}}{2\times 2}$$

Whakareatia -8 ki te 9.

$$m=\frac{-9±\sqrt{81-72}}{2\times 2}$$

Tāpiri 81 ki te -72.

$$m=\frac{-9±\sqrt{9}}{2\times 2}$$

Tuhia te pūtakerua o te 9.

$$m=\frac{-9±3}{2\times 2}$$

Whakareatia 2 ki te 2.

$$m=\frac{-9±3}{4}$$

Nā, me whakaoti te whārite m=\frac{-9±3}{4} ina he tāpiri te ±. Tāpiri -9 ki te 3.

$$m=-\frac{6}{4}$$

Whakahekea te hautanga \frac{-6}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$m=-\frac{3}{2}$$

Nā, me whakaoti te whārite m=\frac{-9±3}{4} ina he tango te ±. Tango 3 mai i -9.

$$m=-\frac{12}{4}$$

Whakawehe -12 ki te 4.

$$m=-3$$

Kua oti te whārite te whakatau.

$$m=-\frac{3}{2} m=-3$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe m ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te m.

$$m\times 9+3mm=m^{2}-9$$

Whakareatia te m ki te m, ka m^{2}.

$$m\times 9+3m^{2}=m^{2}-9$$

Tangohia te m^{2} mai i ngā taha e rua.

$$m\times 9+3m^{2}-m^{2}=-9$$

Pahekotia te 3m^{2} me -m^{2}, ka 2m^{2}.

$$m\times 9+2m^{2}=-9$$

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$2m^{2}+9m=-9$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2m^{2}+9m}{2}=-\frac{9}{2}$$

Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.

$$m^{2}+\frac{9}{2}m=-\frac{9}{2}$$

Whakawehea te \frac{9}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{9}{4}. Nā, tāpiria te pūrua o te \frac{9}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$m^{2}+\frac{9}{2}m+\left(\frac{9}{4}\right)^{2}=-\frac{9}{2}+\left(\frac{9}{4}\right)^{2}$$

Pūruatia \frac{9}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$m^{2}+\frac{9}{2}m+\frac{81}{16}=-\frac{9}{2}+\frac{81}{16}$$

Tāpiri -\frac{9}{2} ki te \frac{81}{16} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$m^{2}+\frac{9}{2}m+\frac{81}{16}=\frac{9}{16}$$

Tauwehea m^{2}+\frac{9}{2}m+\frac{81}{16}. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(m+\frac{9}{4}\right)^{2}=\frac{9}{16}$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$\sqrt{\left(m+\frac{9}{4}\right)^{2}}=\sqrt{\frac{9}{16}}$$

Whakarūnātia.

$$m+\frac{9}{4}=\frac{3}{4} m+\frac{9}{4}=-\frac{3}{4}$$

Me tango \frac{9}{4} mai i ngā taha e rua o te whārite.

$$m=-\frac{3}{2} m=-3$$