Whakaoti i te 6x=sqrt{24+12x}

$$6 x = \sqrt { 24 + 12 x }$$

Whakaoti mō x

$$x=1$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(6x\right)^{2}=\left(\sqrt{24+12x}\right)^{2}$$

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

$$6^{2}x^{2}=\left(\sqrt{24+12x}\right)^{2}$$

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

$$36x^{2}=\left(\sqrt{24+12x}\right)^{2}$$

Tātaihia te \sqrt{24+12x} mā te pū o 2, kia riro ko 24+12x.

$$36x^{2}=24+12x$$

Tangohia te 24 mai i ngā taha e rua.

$$36x^{2}-24=12x$$

Tangohia te 12x mai i ngā taha e rua.

$$36x^{2}-24-12x=0$$

Whakawehea ngā taha e rua ki te 12.

$$3x^{2}-2-x=0$$

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

$$3x^{2}-x-2=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei 3x^{2}+ax+bx-2. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-1 ab=3\left(-2\right)=-6$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōraro te a+b, he nui ake te uara pū o te tau tōraro i tō te tōrunga. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -6.

$$1,-6 2,-3$$

Tātaihia te tapeke mō ia takirua.

$$1-6=-5 2-3=-1$$

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

$$a=-3 b=2$$

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

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

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

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

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

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

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

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

Whakakapia te 1 mō te x i te whārite 6x=\sqrt{24+12x}.

$$6\times 1=\sqrt{24+12\times 1}$$

Whakarūnātia. Ko te uara x=1 kua ngata te whārite.

$$6=6$$

Whakakapia te -\frac{2}{3} mō te x i te whārite 6x=\sqrt{24+12x}.

$$6\left(-\frac{2}{3}\right)=\sqrt{24+12\left(-\frac{2}{3}\right)}$$

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{12x+24} he rongoā ahurei.

$$x=1$$