Whakaoti i te sqrt{-6z+3}+z=-4

$$\sqrt { - 6 z + 3 } + z = - 4$$

Whakaoti mō z

$$z=-13$$

Ngā Upane Otinga

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

$$\sqrt{-6z+3}=-4-z$$

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{-6z+3}\right)^{2}=\left(-4-z\right)^{2}$$

Tātaihia te \sqrt{-6z+3} mā te pū o 2, kia riro ko -6z+3.

$$-6z+3=\left(-4-z\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(-4-z\right)^{2}.

$$-6z+3=16+8z+z^{2}$$

Tangohia te 16 mai i ngā taha e rua.

$$-6z+3-16=8z+z^{2}$$

Tangohia te 16 i te 3, ka -13.

$$-6z-13=8z+z^{2}$$

Tangohia te 8z mai i ngā taha e rua.

$$-6z-13-8z=z^{2}$$

Pahekotia te -6z me -8z, ka -14z.

$$-14z-13=z^{2}$$

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

$$-14z-13-z^{2}=0$$

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

$$-z^{2}-14z-13=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -z^{2}+az+bz-13. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-14 ab=-\left(-13\right)=13$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōraro te a+b, he tōraro hoki a a me b. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=-1 b=-13$$

Tuhia anō te -z^{2}-14z-13 hei \left(-z^{2}-z\right)+\left(-13z-13\right).

$$\left(-z^{2}-z\right)+\left(-13z-13\right)$$

Tauwehea te z i te tuatahi me te 13 i te rōpū tuarua.

$$z\left(-z-1\right)+13\left(-z-1\right)$$

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

$$\left(-z-1\right)\left(z+13\right)$$

Hei kimi otinga whārite, me whakaoti te -z-1=0 me te z+13=0.

$$z=-1 z=-13$$

Whakakapia te -1 mō te z i te whārite \sqrt{-6z+3}+z=-4.

$$\sqrt{-6\left(-1\right)+3}-1=-4$$

Whakarūnātia. Ko te uara z=-1 kāore e ngata ana ki te whārite nā te mea e rerekē ngā tohu o te taha maui me te taha katau.

$$2=-4$$

Whakakapia te -13 mō te z i te whārite \sqrt{-6z+3}+z=-4.

$$\sqrt{-6\left(-13\right)+3}-13=-4$$

Whakarūnātia. Ko te uara z=-13 kua ngata te whārite.

$$-4=-4$$

Ko te whārite \sqrt{3-6z}=-z-4 he rongoā ahurei.

$$z=-13$$