Whakaoti i te x=sqrt{2x-1}

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

Whakaoti mō x

$$x=1$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

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

Tātaihia te \sqrt{2x-1} mā te pū o 2, kia riro ko 2x-1.

$$x^{2}=2x-1$$

Tangohia te 2x mai i ngā taha e rua.

$$x^{2}-2x=-1$$

Me tāpiri te 1 ki ngā taha e rua.

$$x^{2}-2x+1=0$$

Hei whakaoti i te whārite, whakatauwehea te x^{2}-2x+1 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.

$$a+b=-2 ab=1$$

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. Ko te takirua anake pērā ko te otinga pūnaha.

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

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

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

Tuhia anōtia hei pūrua huarua.

$$\left(x-1\right)^{2}$$

Hei kimi i te otinga whārite, whakaotia te x-1=0.

$$x=1$$

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

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

Whakarūnātia. Ko te uara x=1 kua ngata te whārite.

$$1=1$$

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

$$x=1$$