Whakaoti i te sqrt{x+8}=x+2

$$\sqrt { x + 8 } = x + 2$$

Whakaoti mō x

$$x=1$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{x+8}\right)^{2}=\left(x+2\right)^{2}$$

Tātaihia te \sqrt{x+8} mā te pū o 2, kia riro ko x+8.

$$x+8=\left(x+2\right)^{2}$$

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

$$x+8=x^{2}+4x+4$$

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

$$x+8-x^{2}=4x+4$$

Tangohia te 4x mai i ngā taha e rua.

$$x+8-x^{2}-4x=4$$

Pahekotia te x me -4x, ka -3x.

$$-3x+8-x^{2}=4$$

Tangohia te 4 mai i ngā taha e rua.

$$-3x+8-x^{2}-4=0$$

Tangohia te 4 i te 8, ka 4.

$$-3x+4-x^{2}=0$$

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

$$-x^{2}-3x+4=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -x^{2}+ax+bx+4. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-3 ab=-4=-4$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōraro te a+b, he nui ake te uara pū o te tau tōraro i tō te tōrunga. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -4.

$$1,-4 2,-2$$

Tātaihia te tapeke mō ia takirua.

$$1-4=-3 2-2=0$$

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

$$a=1 b=-4$$

Tuhia anō te -x^{2}-3x+4 hei \left(-x^{2}+x\right)+\left(-4x+4\right).

$$\left(-x^{2}+x\right)+\left(-4x+4\right)$$

Tauwehea te x i te tuatahi me te 4 i te rōpū tuarua.

$$x\left(-x+1\right)+4\left(-x+1\right)$$

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

$$\left(-x+1\right)\left(x+4\right)$$

Hei kimi otinga whārite, me whakaoti te -x+1=0 me te x+4=0.

$$x=1 x=-4$$

Whakakapia te 1 mō te x i te whārite \sqrt{x+8}=x+2.

$$\sqrt{1+8}=1+2$$

Whakarūnātia. Ko te uara x=1 kua ngata te whārite.

$$3=3$$

Whakakapia te -4 mō te x i te whārite \sqrt{x+8}=x+2.

$$\sqrt{-4+8}=-4+2$$

Whakarūnātia. Ko te uara x=-4 kāore e ngata ana ki te whārite nā te mea e rerekē ngā tohu o te taha maui me te taha katau.

$$2=-2$$

Ko te whārite \sqrt{x+8}=x+2 he rongoā ahurei.

$$x=1$$