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

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

Whakaoti mō x

$$x=4$$

Ngā Upane Otinga

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

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

Pūruatia ngā taha e rua o te whārite.

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

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

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

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

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

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

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

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(4-2x\right)^{2}.

$$4x=16-16x+4x^{2}$$

Tangohia te 16 mai i ngā taha e rua.

$$4x-16=-16x+4x^{2}$$

Me tāpiri te 16x ki ngā taha e rua.

$$4x-16+16x=4x^{2}$$

Pahekotia te 4x me 16x, ka 20x.

$$20x-16=4x^{2}$$

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

$$20x-16-4x^{2}=0$$

Whakawehea ngā taha e rua ki te 4.

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

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

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

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

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

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

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

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

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

Whakatauwehea atu te kīanga pātahi x-4 mā te whakamahi i te āhuatanga tātai tohatoha.

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

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

$$x=4 x=1$$

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

$$2\times 4-2\sqrt{4}=4$$

Whakarūnātia. Ko te uara x=4 kua ngata te whārite.

$$4=4$$

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

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

Whakarūnātia. Ko te uara x=1 kāore e ngata ana ki te whārite.

$$0=4$$

Ko te whārite -2\sqrt{x}=4-2x he rongoā ahurei.

$$x=4$$