Whakaoti i te sqrt{2z+3}=-z

$$\sqrt { 2 z + 3 } = - z$$

Whakaoti mō z

$$z=-1$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{2z+3}\right)^{2}=\left(-z\right)^{2}$$

Tātaihia te \sqrt{2z+3} mā te pū o 2, kia riro ko 2z+3.

$$2z+3=\left(-z\right)^{2}$$

Tātaihia te -z mā te pū o 2, kia riro ko z^{2}.

$$2z+3=z^{2}$$

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

$$2z+3-z^{2}=0$$

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

$$-z^{2}+2z+3=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -z^{2}+az+bz+3. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=2 ab=-3=-3$$

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.

$$a=3 b=-1$$

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

$$\left(-z^{2}+3z\right)+\left(-z+3\right)$$

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

$$-z\left(z-3\right)-\left(z-3\right)$$

Whakatauwehea atu te kīanga pātahi z-3 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(z-3\right)\left(-z-1\right)$$

Hei kimi otinga whārite, me whakaoti te z-3=0 me te -z-1=0.

$$z=3 z=-1$$

Whakakapia te 3 mō te z i te whārite \sqrt{2z+3}=-z.

$$\sqrt{2\times 3+3}=-3$$

Whakarūnātia. Ko te uara z=3 kāore e ngata ana ki te whārite nā te mea e rerekē ngā tohu o te taha maui me te taha katau.

$$3=-3$$

Whakakapia te -1 mō te z i te whārite \sqrt{2z+3}=-z.

$$\sqrt{2\left(-1\right)+3}=-\left(-1\right)$$

Whakarūnātia. Ko te uara z=-1 kua ngata te whārite.

$$1=1$$

Ko te whārite \sqrt{2z+3}=-z he rongoā ahurei.

$$z=-1$$