Whakaoti i te x-sqrt{3x-2}=4

$$x - \sqrt { 3 x - 2 } = 4$$

Whakaoti mō x

$$x=9$$

Ngā Upane Otinga

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

$$-\sqrt{3x-2}=4-x$$

Pūruatia ngā taha e rua o te whārite.

$$\left(-\sqrt{3x-2}\right)^{2}=\left(4-x\right)^{2}$$

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

$$\left(-1\right)^{2}\left(\sqrt{3x-2}\right)^{2}=\left(4-x\right)^{2}$$

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

$$1\left(\sqrt{3x-2}\right)^{2}=\left(4-x\right)^{2}$$

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

$$1\left(3x-2\right)=\left(4-x\right)^{2}$$

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

$$3x-2=\left(4-x\right)^{2}$$

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

$$3x-2=16-8x+x^{2}$$

Tangohia te 16 mai i ngā taha e rua.

$$3x-2-16=-8x+x^{2}$$

Tangohia te 16 i te -2, ka -18.

$$3x-18=-8x+x^{2}$$

Me tāpiri te 8x ki ngā taha e rua.

$$3x-18+8x=x^{2}$$

Pahekotia te 3x me 8x, ka 11x.

$$11x-18=x^{2}$$

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

$$11x-18-x^{2}=0$$

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

$$-x^{2}+11x-18=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -x^{2}+ax+bx-18. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=11 ab=-\left(-18\right)=18$$

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 18.

$$1,18 2,9 3,6$$

Tātaihia te tapeke mō ia takirua.

$$1+18=19 2+9=11 3+6=9$$

Ko te otinga te takirua ka hoatu i te tapeke 11.

$$a=9 b=2$$

Tuhia anō te -x^{2}+11x-18 hei \left(-x^{2}+9x\right)+\left(2x-18\right).

$$\left(-x^{2}+9x\right)+\left(2x-18\right)$$

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

$$-x\left(x-9\right)+2\left(x-9\right)$$

Whakatauwehea atu te kīanga pātahi x-9 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-9\right)\left(-x+2\right)$$

Hei kimi otinga whārite, me whakaoti te x-9=0 me te -x+2=0.

$$x=9 x=2$$

Whakakapia te 9 mō te x i te whārite x-\sqrt{3x-2}=4.

$$9-\sqrt{3\times 9-2}=4$$

Whakarūnātia. Ko te uara x=9 kua ngata te whārite.

$$4=4$$

Whakakapia te 2 mō te x i te whārite x-\sqrt{3x-2}=4.

$$2-\sqrt{3\times 2-2}=4$$

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

$$0=4$$

Ko te whārite -\sqrt{3x-2}=4-x he rongoā ahurei.

$$x=9$$