Whakaoti i te sqrt{x}=x-6

$$\sqrt { x } = x - 6$$

Whakaoti mō x

$$x=9$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{x}\right)^{2}=\left(x-6\right)^{2}$$

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

$$x=\left(x-6\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-6\right)^{2}.

$$x=x^{2}-12x+36$$

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

$$x-x^{2}=-12x+36$$

Me tāpiri te 12x ki ngā taha e rua.

$$x-x^{2}+12x=36$$

Pahekotia te x me 12x, ka 13x.

$$13x-x^{2}=36$$

Tangohia te 36 mai i ngā taha e rua.

$$13x-x^{2}-36=0$$

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

$$-x^{2}+13x-36=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -x^{2}+ax+bx-36. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=13 ab=-\left(-36\right)=36$$

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 36.

$$1,36 2,18 3,12 4,9 6,6$$

Tātaihia te tapeke mō ia takirua.

$$1+36=37 2+18=20 3+12=15 4+9=13 6+6=12$$

Ko te otinga te takirua ka hoatu i te tapeke 13.

$$a=9 b=4$$

Tuhia anō te -x^{2}+13x-36 hei \left(-x^{2}+9x\right)+\left(4x-36\right).

$$\left(-x^{2}+9x\right)+\left(4x-36\right)$$

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

$$-x\left(x-9\right)+4\left(x-9\right)$$

Whakatauwehea atu te kīanga pātahi x-9 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-9\right)\left(-x+4\right)$$

Hei kimi otinga whārite, me whakaoti te x-9=0 me te -x+4=0.

$$x=9 x=4$$

Whakakapia te 9 mō te x i te whārite \sqrt{x}=x-6.

$$\sqrt{9}=9-6$$

Whakarūnātia. Ko te uara x=9 kua ngata te whārite.

$$3=3$$

Whakakapia te 4 mō te x i te whārite \sqrt{x}=x-6.

$$\sqrt{4}=4-6$$

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}=x-6 he rongoā ahurei.

$$x=9$$