Whakaoti i te 2-sqrt{2x+3}=2x-1

$$2 - \sqrt { 2 x + 3 } = 2 x - 1$$

Whakaoti mō x

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

Ngā Upane Otinga

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

$$-\sqrt{2x+3}=2x-1-2$$

Tangohia te 2 i te -1, ka -3.

$$-\sqrt{2x+3}=2x-3$$

Pūruatia ngā taha e rua o te whārite.

$$\left(-\sqrt{2x+3}\right)^{2}=\left(2x-3\right)^{2}$$

Whakarohaina te \left(-\sqrt{2x+3}\right)^{2}.

$$\left(-1\right)^{2}\left(\sqrt{2x+3}\right)^{2}=\left(2x-3\right)^{2}$$

Tātaihia te -1 mā te pū o 2, kia riro ko 1.

$$1\left(\sqrt{2x+3}\right)^{2}=\left(2x-3\right)^{2}$$

Tātaihia te \sqrt{2x+3} mā te pū o 2, kia riro ko 2x+3.

$$1\left(2x+3\right)=\left(2x-3\right)^{2}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 1 ki te 2x+3.

$$2x+3=\left(2x-3\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(2x-3\right)^{2}.

$$2x+3=4x^{2}-12x+9$$

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

$$2x+3-4x^{2}=-12x+9$$

Me tāpiri te 12x ki ngā taha e rua.

$$2x+3-4x^{2}+12x=9$$

Pahekotia te 2x me 12x, ka 14x.

$$14x+3-4x^{2}=9$$

Tangohia te 9 mai i ngā taha e rua.

$$14x+3-4x^{2}-9=0$$

Tangohia te 9 i te 3, ka -6.

$$14x-6-4x^{2}=0$$

Whakawehea ngā taha e rua ki te 2.

$$7x-3-2x^{2}=0$$

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

$$-2x^{2}+7x-3=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -2x^{2}+ax+bx-3. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=7 ab=-2\left(-3\right)=6$$

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 6.

$$1,6 2,3$$

Tātaihia te tapeke mō ia takirua.

$$1+6=7 2+3=5$$

Ko te otinga te takirua ka hoatu i te tapeke 7.

$$a=6 b=1$$

Tuhia anō te -2x^{2}+7x-3 hei \left(-2x^{2}+6x\right)+\left(x-3\right).

$$\left(-2x^{2}+6x\right)+\left(x-3\right)$$

Tauwehea te 2x i te tuatahi me te -1 i te rōpū tuarua.

$$2x\left(-x+3\right)-\left(-x+3\right)$$

Whakatauwehea atu te kīanga pātahi -x+3 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(-x+3\right)\left(2x-1\right)$$

Hei kimi otinga whārite, me whakaoti te -x+3=0 me te 2x-1=0.

$$x=3 x=\frac{1}{2}$$

Whakakapia te 3 mō te x i te whārite 2-\sqrt{2x+3}=2x-1.

$$2-\sqrt{2\times 3+3}=2\times 3-1$$

Whakarūnātia. Ko te uara x=3 kāore e ngata ana ki te whārite nā te mea e rerekē ngā tohu o te taha maui me te taha katau.

$$-1=5$$

Whakakapia te \frac{1}{2} mō te x i te whārite 2-\sqrt{2x+3}=2x-1.

$$2-\sqrt{2\times \frac{1}{2}+3}=2\times \frac{1}{2}-1$$

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

$$0=0$$

Ko te whārite -\sqrt{2x+3}=2x-3 he rongoā ahurei.

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