Whakaoti i te z^2=-1-2z

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

Whakaoti mō z

$$z=-1$$

Ngā Upane Whakamahi Tauwehe

Tangohia te -1 mai i ngā taha e rua.

$$z^{2}-\left(-1\right)=-2z$$

Ko te tauaro o -1 ko 1.

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

Me tāpiri te 2z ki ngā taha e rua.

$$z^{2}+1+2z=0$$

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

$$z^{2}+2z+1=0$$

Hei whakaoti i te whārite, whakatauwehea te z^{2}+2z+1 mā te whakamahi i te tātai z^{2}+\left(a+b\right)z+ab=\left(z+a\right)\left(z+b\right). Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

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

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.

$$a=1 b=1$$

Me tuhi anō te kīanga whakatauwehe \left(z+a\right)\left(z+b\right) mā ngā uara i tātaihia.

$$\left(z+1\right)\left(z+1\right)$$

Tuhia anōtia hei pūrua huarua.

$$\left(z+1\right)^{2}$$

Hei kimi i te otinga whārite, whakaotia te z+1=0.

$$z=-1$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Tangohia te -1 mai i ngā taha e rua.

$$z^{2}-\left(-1\right)=-2z$$

Ko te tauaro o -1 ko 1.

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

Me tāpiri te 2z ki ngā taha e rua.

$$z^{2}+1+2z=0$$

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

$$z^{2}+2z+1=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei z^{2}+az+bz+1. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=2 ab=1\times 1=1$$

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.

$$a=1 b=1$$

Tuhia anō te z^{2}+2z+1 hei \left(z^{2}+z\right)+\left(z+1\right).

$$\left(z^{2}+z\right)+\left(z+1\right)$$

Whakatauwehea atu z i te z^{2}+z.

$$z\left(z+1\right)+z+1$$

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

$$\left(z+1\right)\left(z+1\right)$$

Tuhia anōtia hei pūrua huarua.

$$\left(z+1\right)^{2}$$

Hei kimi i te otinga whārite, whakaotia te z+1=0.

$$z=-1$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te -1 mai i ngā taha e rua.

$$z^{2}-\left(-1\right)=-2z$$

Ko te tauaro o -1 ko 1.

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

Me tāpiri te 2z ki ngā taha e rua.

$$z^{2}+1+2z=0$$

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.

$$z^{2}+2z+1=0$$

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

$$z=\frac{-2±\sqrt{2^{2}-4}}{2}$$

Pūrua 2.

$$z=\frac{-2±\sqrt{4-4}}{2}$$

Tāpiri 4 ki te -4.

$$z=\frac{-2±\sqrt{0}}{2}$$

Tuhia te pūtakerua o te 0.

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

Whakawehe -2 ki te 2.

$$z=-1$$

Ngā Upane mō te Whakaoti i te Pūrua

Me tāpiri te 2z ki ngā taha e rua.

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

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

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

Pūrua 1.

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

Tāpiri -1 ki te 1.

$$z^{2}+2z+1=0$$

Tauwehea z^{2}+2z+1. 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}.

$$\left(z+1\right)^{2}=0$$

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

$$\sqrt{\left(z+1\right)^{2}}=\sqrt{0}$$

Whakarūnātia.

$$z+1=0 z+1=0$$

Me tango 1 mai i ngā taha e rua o te whārite.

$$z=-1 z=-1$$

Kua oti te whārite te whakatau. He ōrite ngā whakatau.

$$z=-1$$