Whakaoti i te 4x=sqrt{12x-2}

$$4 x = \sqrt { 12 x - 2 }$$

Whakaoti mō x

$$x=\frac{1}{2}=0.5$$

$$x=\frac{1}{4}=0.25$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(4x\right)^{2}=\left(\sqrt{12x-2}\right)^{2}$$

Whakarohaina te \left(4x\right)^{2}.

$$4^{2}x^{2}=\left(\sqrt{12x-2}\right)^{2}$$

Tātaihia te 4 mā te pū o 2, kia riro ko 16.

$$16x^{2}=\left(\sqrt{12x-2}\right)^{2}$$

Tātaihia te \sqrt{12x-2} mā te pū o 2, kia riro ko 12x-2.

$$16x^{2}=12x-2$$

Tangohia te 12x mai i ngā taha e rua.

$$16x^{2}-12x=-2$$

Me tāpiri te 2 ki ngā taha e rua.

$$16x^{2}-12x+2=0$$

Whakawehea ngā taha e rua ki te 2.

$$8x^{2}-6x+1=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei 8x^{2}+ax+bx+1. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-6 ab=8\times 1=8$$

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 8.

$$-1,-8 -2,-4$$

Tātaihia te tapeke mō ia takirua.

$$-1-8=-9 -2-4=-6$$

Ko te otinga te takirua ka hoatu i te tapeke -6.

$$a=-4 b=-2$$

Tuhia anō te 8x^{2}-6x+1 hei \left(8x^{2}-4x\right)+\left(-2x+1\right).

$$\left(8x^{2}-4x\right)+\left(-2x+1\right)$$

Tauwehea te 4x i te tuatahi me te -1 i te rōpū tuarua.

$$4x\left(2x-1\right)-\left(2x-1\right)$$

Whakatauwehea atu te kīanga pātahi 2x-1 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(2x-1\right)\left(4x-1\right)$$

Hei kimi otinga whārite, me whakaoti te 2x-1=0 me te 4x-1=0.

$$x=\frac{1}{2} x=\frac{1}{4}$$

Whakakapia te \frac{1}{2} mō te x i te whārite 4x=\sqrt{12x-2}.

$$4\times \frac{1}{2}=\sqrt{12\times \frac{1}{2}-2}$$

Whakarūnātia. Ko te uara x=\frac{1}{2} kua ngata te whārite.

$$2=2$$

Whakakapia te \frac{1}{4} mō te x i te whārite 4x=\sqrt{12x-2}.

$$4\times \frac{1}{4}=\sqrt{12\times \frac{1}{4}-2}$$

Whakarūnātia. Ko te uara x=\frac{1}{4} kua ngata te whārite.

$$1=1$$

Rārangihia ngā rongoā katoa o 4x=\sqrt{12x-2}.

$$x=\frac{1}{2} x=\frac{1}{4}$$