Whakaoti i te n+1=n^2-1

$$n + 1 = n ^ { 2 } - 1$$

Whakaoti mō n

$$n=-1$$

$$n=2$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

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

$$n+1-n^{2}=-1$$

Me tāpiri te 1 ki ngā taha e rua.

$$n+1-n^{2}+1=0$$

Tāpirihia te 1 ki te 1, ka 2.

$$n+2-n^{2}=0$$

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

$$-n^{2}+n+2=0$$

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

$$a+b=1 ab=-2=-2$$

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. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=2 b=-1$$

Tuhia anō te -n^{2}+n+2 hei \left(-n^{2}+2n\right)+\left(-n+2\right).

$$\left(-n^{2}+2n\right)+\left(-n+2\right)$$

Tauwehea te -n i te tuatahi me te -1 i te rōpū tuarua.

$$-n\left(n-2\right)-\left(n-2\right)$$

Whakatauwehea atu te kīanga pātahi n-2 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(n-2\right)\left(-n-1\right)$$

Hei kimi otinga whārite, me whakaoti te n-2=0 me te -n-1=0.

$$n=2 n=-1$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$n+1-n^{2}=-1$$

Me tāpiri te 1 ki ngā taha e rua.

$$n+1-n^{2}+1=0$$

Tāpirihia te 1 ki te 1, ka 2.

$$n+2-n^{2}=0$$

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.

$$-n^{2}+n+2=0$$

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

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

Pūrua 1.

$$n=\frac{-1±\sqrt{1-4\left(-1\right)\times 2}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$n=\frac{-1±\sqrt{1+4\times 2}}{2\left(-1\right)}$$

Whakareatia 4 ki te 2.

$$n=\frac{-1±\sqrt{1+8}}{2\left(-1\right)}$$

Tāpiri 1 ki te 8.

$$n=\frac{-1±\sqrt{9}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 9.

$$n=\frac{-1±3}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$n=\frac{-1±3}{-2}$$

Nā, me whakaoti te whārite n=\frac{-1±3}{-2} ina he tāpiri te ±. Tāpiri -1 ki te 3.

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

Whakawehe 2 ki te -2.

$$n=-1$$

Nā, me whakaoti te whārite n=\frac{-1±3}{-2} ina he tango te ±. Tango 3 mai i -1.

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

Whakawehe -4 ki te -2.

$$n=2$$

Kua oti te whārite te whakatau.

$$n=-1 n=2$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$n+1-n^{2}=-1$$

Tangohia te 1 mai i ngā taha e rua.

$$n-n^{2}=-1-1$$

Tangohia te 1 i te -1, ka -2.

$$n-n^{2}=-2$$

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.

$$-n^{2}+n=-2$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-n^{2}+n}{-1}=-\frac{2}{-1}$$

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

$$n^{2}+\frac{1}{-1}n=-\frac{2}{-1}$$

Whakawehe 1 ki te -1.

$$n^{2}-n=-\frac{2}{-1}$$

Whakawehe -2 ki te -1.

$$n^{2}-n=2$$

Whakawehea te -1, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{1}{2}. Nā, tāpiria te pūrua o te -\frac{1}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$n^{2}-n+\left(-\frac{1}{2}\right)^{2}=2+\left(-\frac{1}{2}\right)^{2}$$

Pūruatia -\frac{1}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$n^{2}-n+\frac{1}{4}=2+\frac{1}{4}$$

Tāpiri 2 ki te \frac{1}{4}.

$$n^{2}-n+\frac{1}{4}=\frac{9}{4}$$

Tauwehea n^{2}-n+\frac{1}{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}.

$$\left(n-\frac{1}{2}\right)^{2}=\frac{9}{4}$$

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

$$\sqrt{\left(n-\frac{1}{2}\right)^{2}}=\sqrt{\frac{9}{4}}$$

Whakarūnātia.

$$n-\frac{1}{2}=\frac{3}{2} n-\frac{1}{2}=-\frac{3}{2}$$

Me tāpiri \frac{1}{2} ki ngā taha e rua o te whārite.

$$n=2 n=-1$$