Whakaoti i te sqrt{x+2}+1=sqrt{3x+3}

$$\sqrt { x + 2 } + 1 = \sqrt { 3 x + 3 }$$

Whakaoti mō x

$$x=2$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

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

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(\sqrt{x+2}+1\right)^{2}.

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

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

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

Tāpirihia te 2 ki te 1, ka 3.

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

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

$$x+3+2\sqrt{x+2}=3x+3$$

Me tango x+3 mai i ngā taha e rua o te whārite.

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

Hei kimi i te tauaro o x+3, kimihia te tauaro o ia taurangi.

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

Pahekotia te 3x me -x, ka 2x.

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

Tangohia te 3 i te 3, ka 0.

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

Me whakakore te 2 ki ngā taha e rua.

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

Pūruatia ngā taha e rua o te whārite.

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

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

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

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

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

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

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

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -x^{2}+ax+bx+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 -x^{2}+x+2 hei \left(-x^{2}+2x\right)+\left(-x+2\right).

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

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

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

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

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

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

$$x=2 x=-1$$

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

$$\sqrt{2+2}+1=\sqrt{3\times 2+3}$$

Whakarūnātia. Ko te uara x=2 kua ngata te whārite.

$$3=3$$

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

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

Whakarūnātia. Ko te uara x=-1 kāore e ngata ana ki te whārite.

$$2=0$$

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

$$\sqrt{2+2}+1=\sqrt{3\times 2+3}$$

Whakarūnātia. Ko te uara x=2 kua ngata te whārite.

$$3=3$$

Ko te whārite \sqrt{x+2}+1=\sqrt{3x+3} he rongoā ahurei.

$$x=2$$