Whakaoti i te x-2=sqrt{x}

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

Whakaoti mō x

$$x=4$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

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

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

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

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

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

Tangohia te x mai i ngā taha e rua.

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

Pahekotia te -4x me -x, ka -5x.

$$x^{2}-5x+4=0$$

Hei whakaoti i te whārite, whakatauwehea te x^{2}-5x+4 mā te whakamahi i te tātai x^{2}+\left(a+b\right)x+ab=\left(x+a\right)\left(x+b\right). Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-5 ab=4$$

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. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 4.

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

Tātaihia te tapeke mō ia takirua.

$$-1-4=-5 -2-2=-4$$

Ko te otinga te takirua ka hoatu i te tapeke -5.

$$a=-4 b=-1$$

Me tuhi anō te kīanga whakatauwehe \left(x+a\right)\left(x+b\right) mā ngā uara i tātaihia.

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

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

$$x=4 x=1$$

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

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

Whakarūnātia. Ko te uara x=4 kua ngata te whārite.

$$2=2$$

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

$$1-2=\sqrt{1}$$

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

$$-1=1$$

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

$$x=4$$