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

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

Whakaoti mō x

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

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

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

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

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

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(-2x+1\right)^{2}.

$$x=4x^{2}-4x+1$$

Tangohia te 4x^{2} mai i ngā taha e rua.

$$x-4x^{2}=-4x+1$$

Me tāpiri te 4x ki ngā taha e rua.

$$x-4x^{2}+4x=1$$

Pahekotia te x me 4x, ka 5x.

$$5x-4x^{2}=1$$

Tangohia te 1 mai i ngā taha e rua.

$$5x-4x^{2}-1=0$$

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

$$-4x^{2}+5x-1=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -4x^{2}+ax+bx-1. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=5 ab=-4\left(-1\right)=4$$

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 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.

$$a=4 b=1$$

Tuhia anō te -4x^{2}+5x-1 hei \left(-4x^{2}+4x\right)+\left(x-1\right).

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

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

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

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

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

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

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

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

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

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.

$$1=-1$$

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

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

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

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

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

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