Whakaoti i te 3x=sqrt{8+6x}

$$3 x = \sqrt { 8 + 6 x }$$

Whakaoti mō x

$$x = \frac{4}{3} = 1\frac{1}{3} \approx 1.333333333$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(3x\right)^{2}=\left(\sqrt{8+6x}\right)^{2}$$

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

$$3^{2}x^{2}=\left(\sqrt{8+6x}\right)^{2}$$

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

$$9x^{2}=\left(\sqrt{8+6x}\right)^{2}$$

Tātaihia te \sqrt{8+6x} mā te pū o 2, kia riro ko 8+6x.

$$9x^{2}=8+6x$$

Tangohia te 8 mai i ngā taha e rua.

$$9x^{2}-8=6x$$

Tangohia te 6x mai i ngā taha e rua.

$$9x^{2}-8-6x=0$$

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

$$9x^{2}-6x-8=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei 9x^{2}+ax+bx-8. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-6 ab=9\left(-8\right)=-72$$

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 -72.

$$1,-72 2,-36 3,-24 4,-18 6,-12 8,-9$$

Tātaihia te tapeke mō ia takirua.

$$1-72=-71 2-36=-34 3-24=-21 4-18=-14 6-12=-6 8-9=-1$$

Ko te otinga te takirua ka hoatu i te tapeke -6.

$$a=-12 b=6$$

Tuhia anō te 9x^{2}-6x-8 hei \left(9x^{2}-12x\right)+\left(6x-8\right).

$$\left(9x^{2}-12x\right)+\left(6x-8\right)$$

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

$$3x\left(3x-4\right)+2\left(3x-4\right)$$

Whakatauwehea atu te kīanga pātahi 3x-4 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(3x-4\right)\left(3x+2\right)$$

Hei kimi otinga whārite, me whakaoti te 3x-4=0 me te 3x+2=0.

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

Whakakapia te \frac{4}{3} mō te x i te whārite 3x=\sqrt{8+6x}.

$$3\times \frac{4}{3}=\sqrt{8+6\times \frac{4}{3}}$$

Whakarūnātia. Ko te uara x=\frac{4}{3} kua ngata te whārite.

$$4=4$$

Whakakapia te -\frac{2}{3} mō te x i te whārite 3x=\sqrt{8+6x}.

$$3\left(-\frac{2}{3}\right)=\sqrt{8+6\left(-\frac{2}{3}\right)}$$

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.

$$-2=2$$

Ko te whārite 3x=\sqrt{6x+8} he rongoā ahurei.

$$x=\frac{4}{3}$$