Whakaoti i te sqrt{3x+6}=3x

$$\sqrt { 3 x + 6 } = 3 x$$

Whakaoti mō x

$$x=1$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{3x+6}\right)^{2}=\left(3x\right)^{2}$$

Tātaihia te \sqrt{3x+6} mā te pū o 2, kia riro ko 3x+6.

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

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

$$3x+6=3^{2}x^{2}$$

Tātaihia te 3 mā te pū o 2, kia riro ko 9.

$$3x+6=9x^{2}$$

Tangohia te 9x^{2} mai i ngā taha e rua.

$$3x+6-9x^{2}=0$$

Whakawehea ngā taha e rua ki te 3.

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

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

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

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.

$$a+b=1 ab=-3\times 2=-6$$

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 -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 \sqrt{3x+6}=3x.

$$\sqrt{3\times 1+6}=3\times 1$$

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

$$3=3$$

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

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

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.

$$2=-2$$

Ko te whārite \sqrt{3x+6}=3x he rongoā ahurei.

$$x=1$$