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

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

Whakaoti mō x

$$x=3$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

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

Tātaihia te \sqrt{4+2x-x^{2}} mā te pū o 2, kia riro ko 4+2x-x^{2}.

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

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

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

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

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

Pahekotia te -x^{2} me -x^{2}, ka -2x^{2}.

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

Me tāpiri te 4x ki ngā taha e rua.

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

Pahekotia te 2x me 4x, ka 6x.

$$4+6x-2x^{2}=4$$

Tangohia te 4 mai i ngā taha e rua.

$$4+6x-2x^{2}-4=0$$

Tangohia te 4 i te 4, ka 0.

$$6x-2x^{2}=0$$

Tauwehea te x.

$$x\left(6-2x\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 6-2x=0.

$$x=0 x=3$$

Whakakapia te 0 mō te x i te whārite \sqrt{4+2x-x^{2}}=x-2.

$$\sqrt{4+2\times 0-0^{2}}=0-2$$

Whakarūnātia. Ko te uara x=0 kāore e ngata ana ki te whārite nā te mea e rerekē ngā tohu o te taha maui me te taha katau.

$$2=-2$$

Whakakapia te 3 mō te x i te whārite \sqrt{4+2x-x^{2}}=x-2.

$$\sqrt{4+2\times 3-3^{2}}=3-2$$

Whakarūnātia. Ko te uara x=3 kua ngata te whārite.

$$1=1$$

Ko te whārite \sqrt{4+2x-x^{2}}=x-2 he rongoā ahurei.

$$x=3$$