Whakaoti i te 9+3m=m^2-1

$$9 + 3 m = m ^ { 2 } - 1$$

Whakaoti mō m

$$m=-2$$

$$m=5$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

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

$$9+3m-m^{2}=-1$$

Me tāpiri te 1 ki ngā taha e rua.

$$9+3m-m^{2}+1=0$$

Tāpirihia te 9 ki te 1, ka 10.

$$10+3m-m^{2}=0$$

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

$$-m^{2}+3m+10=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -m^{2}+am+bm+10. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=3 ab=-10=-10$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -10.

$$-1,10 -2,5$$

Tātaihia te tapeke mō ia takirua.

$$-1+10=9 -2+5=3$$

Ko te otinga te takirua ka hoatu i te tapeke 3.

$$a=5 b=-2$$

Tuhia anō te -m^{2}+3m+10 hei \left(-m^{2}+5m\right)+\left(-2m+10\right).

$$\left(-m^{2}+5m\right)+\left(-2m+10\right)$$

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

$$-m\left(m-5\right)-2\left(m-5\right)$$

Whakatauwehea atu te kīanga pātahi m-5 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(m-5\right)\left(-m-2\right)$$

Hei kimi otinga whārite, me whakaoti te m-5=0 me te -m-2=0.

$$m=5 m=-2$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$9+3m-m^{2}=-1$$

Me tāpiri te 1 ki ngā taha e rua.

$$9+3m-m^{2}+1=0$$

Tāpirihia te 9 ki te 1, ka 10.

$$10+3m-m^{2}=0$$

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.

$$-m^{2}+3m+10=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 3 mō b, me 10 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{-3±\sqrt{3^{2}-4\left(-1\right)\times 10}}{2\left(-1\right)}$$

Pūrua 3.

$$m=\frac{-3±\sqrt{9-4\left(-1\right)\times 10}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$m=\frac{-3±\sqrt{9+4\times 10}}{2\left(-1\right)}$$

Whakareatia 4 ki te 10.

$$m=\frac{-3±\sqrt{9+40}}{2\left(-1\right)}$$

Tāpiri 9 ki te 40.

$$m=\frac{-3±\sqrt{49}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 49.

$$m=\frac{-3±7}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$m=\frac{-3±7}{-2}$$

Nā, me whakaoti te whārite m=\frac{-3±7}{-2} ina he tāpiri te ±. Tāpiri -3 ki te 7.

$$m=\frac{4}{-2}$$

Whakawehe 4 ki te -2.

$$m=-2$$

Nā, me whakaoti te whārite m=\frac{-3±7}{-2} ina he tango te ±. Tango 7 mai i -3.

$$m=-\frac{10}{-2}$$

Whakawehe -10 ki te -2.

$$m=5$$

Kua oti te whārite te whakatau.

$$m=-2 m=5$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$9+3m-m^{2}=-1$$

Tangohia te 9 mai i ngā taha e rua.

$$3m-m^{2}=-1-9$$

Tangohia te 9 i te -1, ka -10.

$$3m-m^{2}=-10$$

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.

$$-m^{2}+3m=-10$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-m^{2}+3m}{-1}=-\frac{10}{-1}$$

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

$$m^{2}+\frac{3}{-1}m=-\frac{10}{-1}$$

Whakawehe 3 ki te -1.

$$m^{2}-3m=-\frac{10}{-1}$$

Whakawehe -10 ki te -1.

$$m^{2}-3m=10$$

Whakawehea te -3, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{3}{2}. Nā, tāpiria te pūrua o te -\frac{3}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$m^{2}-3m+\left(-\frac{3}{2}\right)^{2}=10+\left(-\frac{3}{2}\right)^{2}$$

Pūruatia -\frac{3}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$m^{2}-3m+\frac{9}{4}=10+\frac{9}{4}$$

Tāpiri 10 ki te \frac{9}{4}.

$$m^{2}-3m+\frac{9}{4}=\frac{49}{4}$$

Tauwehea m^{2}-3m+\frac{9}{4}. 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}.

$$\left(m-\frac{3}{2}\right)^{2}=\frac{49}{4}$$

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

$$\sqrt{\left(m-\frac{3}{2}\right)^{2}}=\sqrt{\frac{49}{4}}$$

Whakarūnātia.

$$m-\frac{3}{2}=\frac{7}{2} m-\frac{3}{2}=-\frac{7}{2}$$

Me tāpiri \frac{3}{2} ki ngā taha e rua o te whārite.

$$m=5 m=-2$$