Whakaoti i te sqrt{-2x+5}=2x-3

$$\sqrt{ -2x+5 } =2x-3$$

Whakaoti mō x

$$x=2$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{-2x+5}\right)^{2}=\left(2x-3\right)^{2}$$

Tātaihia te \sqrt{-2x+5} mā te pū o 2, kia riro ko -2x+5.

$$-2x+5=\left(2x-3\right)^{2}$$

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

$$-2x+5=4x^{2}-12x+9$$

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

$$-2x+5-4x^{2}=-12x+9$$

Me tāpiri te 12x ki ngā taha e rua.

$$-2x+5-4x^{2}+12x=9$$

Pahekotia te -2x me 12x, ka 10x.

$$10x+5-4x^{2}=9$$

Tangohia te 9 mai i ngā taha e rua.

$$10x+5-4x^{2}-9=0$$

Tangohia te 9 i te 5, ka -4.

$$10x-4-4x^{2}=0$$

Whakawehea ngā taha e rua ki te 2.

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

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

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

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

$$a+b=5 ab=-2\left(-2\right)=4$$

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

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

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

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

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

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

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

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

Whakakapia te 2 mō te x i te whārite \sqrt{-2x+5}=2x-3.

$$\sqrt{-2\times 2+5}=2\times 2-3$$

Whakarūnātia. Ko te uara x=2 kua ngata te whārite.

$$1=1$$

Whakakapia te \frac{1}{2} mō te x i te whārite \sqrt{-2x+5}=2x-3.

$$\sqrt{-2\times \frac{1}{2}+5}=2\times \frac{1}{2}-3$$

Whakarūnātia. Ko te uara x=\frac{1}{2} kāore e ngata ana ki te whārite nā te mea e rerekē ngā tohu o te taha maui me te taha katau.

$$2=-2$$

Ko te whārite \sqrt{5-2x}=2x-3 he rongoā ahurei.

$$x=2$$