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

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

Whakaoti mō x

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

Ngā Upane Otinga

Me tāpiri te \sqrt{2-x} ki ngā taha e rua.

$$2x-1+\sqrt{2-x}=0$$

Me tāpiri te 1 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

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

Me tango 2x mai i ngā taha e rua o te whārite.

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

Pūruatia ngā taha e rua o te whārite.

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

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

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

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

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

Me tāpiri te 4x ki ngā taha e rua.

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

Pahekotia te -x me 4x, ka 3x.

$$2+3x=1+4x^{2}$$

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

$$2+3x-4x^{2}=1$$

Tangohia te 1 mai i ngā taha e rua.

$$2+3x-4x^{2}-1=0$$

Tangohia te 1 i te 2, ka 1.

$$1+3x-4x^{2}=0$$

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

$$-4x^{2}+3x+1=0$$

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.

$$a+b=3 ab=-4=-4$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -4.

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

Tātaihia te tapeke mō ia takirua.

$$-1+4=3 -2+2=0$$

Ko te otinga te takirua ka hoatu i te tapeke 3.

$$a=4 b=-1$$

Tuhia anō te -4x^{2}+3x+1 hei \left(-4x^{2}+4x\right)+\left(-x+1\right).

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

Whakatauwehea atu 4x i te -4x^{2}+4x.

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

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

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

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

$$2\left(-\frac{1}{4}\right)-1=-\sqrt{2-\left(-\frac{1}{4}\right)}$$

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

$$-\frac{3}{2}=-\frac{3}{2}$$

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

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