Whakaoti i te sqrt{x+2}=x-4

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

Whakaoti mō x

$$x=7$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

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

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

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

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

$$x+2=x^{2}-8x+16$$

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

$$x+2-x^{2}=-8x+16$$

Me tāpiri te 8x ki ngā taha e rua.

$$x+2-x^{2}+8x=16$$

Pahekotia te x me 8x, ka 9x.

$$9x+2-x^{2}=16$$

Tangohia te 16 mai i ngā taha e rua.

$$9x+2-x^{2}-16=0$$

Tangohia te 16 i te 2, ka -14.

$$9x-14-x^{2}=0$$

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

$$-x^{2}+9x-14=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -x^{2}+ax+bx-14. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=9 ab=-\left(-14\right)=14$$

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. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 14.

$$1,14 2,7$$

Tātaihia te tapeke mō ia takirua.

$$1+14=15 2+7=9$$

Ko te otinga te takirua ka hoatu i te tapeke 9.

$$a=7 b=2$$

Tuhia anō te -x^{2}+9x-14 hei \left(-x^{2}+7x\right)+\left(2x-14\right).

$$\left(-x^{2}+7x\right)+\left(2x-14\right)$$

Tauwehea te -x i te tuatahi me te 2 i te rōpū tuarua.

$$-x\left(x-7\right)+2\left(x-7\right)$$

Whakatauwehea atu te kīanga pātahi x-7 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-7\right)\left(-x+2\right)$$

Hei kimi otinga whārite, me whakaoti te x-7=0 me te -x+2=0.

$$x=7 x=2$$

Whakakapia te 7 mō te x i te whārite \sqrt{x+2}=x-4.

$$\sqrt{7+2}=7-4$$

Whakarūnātia. Ko te uara x=7 kua ngata te whārite.

$$3=3$$

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

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

Whakarūnātia. Ko te uara x=2 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+2}=x-4 he rongoā ahurei.

$$x=7$$