Whakaoti i te 6x=sqrt{12-6x}

$$6 x = \sqrt { 12 - 6 x }$$

Whakaoti mō x

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

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(6x\right)^{2}=\left(\sqrt{12-6x}\right)^{2}$$

Whakarohaina te \left(6x\right)^{2}.

$$6^{2}x^{2}=\left(\sqrt{12-6x}\right)^{2}$$

Tātaihia te 6 mā te pū o 2, kia riro ko 36.

$$36x^{2}=\left(\sqrt{12-6x}\right)^{2}$$

Tātaihia te \sqrt{12-6x} mā te pū o 2, kia riro ko 12-6x.

$$36x^{2}=12-6x$$

Tangohia te 12 mai i ngā taha e rua.

$$36x^{2}-12=-6x$$

Me tāpiri te 6x ki ngā taha e rua.

$$36x^{2}-12+6x=0$$

Whakawehea ngā taha e rua ki te 6.

$$6x^{2}-2+x=0$$

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

$$6x^{2}+x-2=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei 6x^{2}+ax+bx-2. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=1 ab=6\left(-2\right)=-12$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -12.

$$-1,12 -2,6 -3,4$$

Tātaihia te tapeke mō ia takirua.

$$-1+12=11 -2+6=4 -3+4=1$$

Ko te otinga te takirua ka hoatu i te tapeke 1.

$$a=-3 b=4$$

Tuhia anō te 6x^{2}+x-2 hei \left(6x^{2}-3x\right)+\left(4x-2\right).

$$\left(6x^{2}-3x\right)+\left(4x-2\right)$$

Tauwehea te 3x i te tuatahi me te 2 i te rōpū tuarua.

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

Whakatauwehea atu te kīanga pātahi 2x-1 mā te whakamahi i te āhuatanga tātai tohatoha.

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

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

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

Whakakapia te \frac{1}{2} mō te x i te whārite 6x=\sqrt{12-6x}.

$$6\times \frac{1}{2}=\sqrt{12-6\times \frac{1}{2}}$$

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

$$3=3$$

Whakakapia te -\frac{2}{3} mō te x i te whārite 6x=\sqrt{12-6x}.

$$6\left(-\frac{2}{3}\right)=\sqrt{12-6\left(-\frac{2}{3}\right)}$$

Whakarūnātia. Ko te uara x=-\frac{2}{3} kāore e ngata ana ki te whārite nā te mea e rerekē ngā tohu o te taha maui me te taha katau.

$$-4=4$$

Ko te whārite 6x=\sqrt{12-6x} he rongoā ahurei.

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