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

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

Whakaoti mō x

$$x=8$$

Ngā Upane Otinga

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

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

Pūruatia ngā taha e rua o te whārite.

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

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

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

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

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

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

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

Whakareatia te 1 ki te 2, ka 2.

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

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

$$2x=16-8x+x^{2}$$

Tangohia te 16 mai i ngā taha e rua.

$$2x-16=-8x+x^{2}$$

Me tāpiri te 8x ki ngā taha e rua.

$$2x-16+8x=x^{2}$$

Pahekotia te 2x me 8x, ka 10x.

$$10x-16=x^{2}$$

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

$$10x-16-x^{2}=0$$

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

$$-x^{2}+10x-16=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -x^{2}+ax+bx-16. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=10 ab=-\left(-16\right)=16$$

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 16.

$$1,16 2,8 4,4$$

Tātaihia te tapeke mō ia takirua.

$$1+16=17 2+8=10 4+4=8$$

Ko te otinga te takirua ka hoatu i te tapeke 10.

$$a=8 b=2$$

Tuhia anō te -x^{2}+10x-16 hei \left(-x^{2}+8x\right)+\left(2x-16\right).

$$\left(-x^{2}+8x\right)+\left(2x-16\right)$$

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

$$-x\left(x-8\right)+2\left(x-8\right)$$

Whakatauwehea atu te kīanga pātahi x-8 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-8\right)\left(-x+2\right)$$

Hei kimi otinga whārite, me whakaoti te x-8=0 me te -x+2=0.

$$x=8 x=2$$

Whakakapia te 8 mō te x i te whārite x-\sqrt{2x}=4.

$$8-\sqrt{2\times 8}=4$$

Whakarūnātia. Ko te uara x=8 kua ngata te whārite.

$$4=4$$

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

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

Whakarūnātia. Ko te uara x=2 kāore e ngata ana ki te whārite.

$$0=4$$

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

$$x=8$$