Whakaoti i te sqrt{4-9x}=3x

$$\sqrt { 4 - 9 x } = 3 x$$

Whakaoti mō x

$$x=\frac{1}{3}\approx 0.333333333$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{4-9x}\right)^{2}=\left(3x\right)^{2}$$

Tātaihia te \sqrt{4-9x} mā te pū o 2, kia riro ko 4-9x.

$$4-9x=\left(3x\right)^{2}$$

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

$$4-9x=3^{2}x^{2}$$

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

$$4-9x=9x^{2}$$

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

$$4-9x-9x^{2}=0$$

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

$$-9x^{2}-9x+4=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -9x^{2}+ax+bx+4. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-9 ab=-9\times 4=-36$$

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 -36.

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

Tātaihia te tapeke mō ia takirua.

$$1-36=-35 2-18=-16 3-12=-9 4-9=-5 6-6=0$$

Ko te otinga te takirua ka hoatu i te tapeke -9.

$$a=3 b=-12$$

Tuhia anō te -9x^{2}-9x+4 hei \left(-9x^{2}+3x\right)+\left(-12x+4\right).

$$\left(-9x^{2}+3x\right)+\left(-12x+4\right)$$

Tauwehea te 3x i te tuatahi me te 4 i te rōpū tuarua.

$$3x\left(-3x+1\right)+4\left(-3x+1\right)$$

Whakatauwehea atu te kīanga pātahi -3x+1 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(-3x+1\right)\left(3x+4\right)$$

Hei kimi otinga whārite, me whakaoti te -3x+1=0 me te 3x+4=0.

$$x=\frac{1}{3} x=-\frac{4}{3}$$

Whakakapia te \frac{1}{3} mō te x i te whārite \sqrt{4-9x}=3x.

$$\sqrt{4-9\times \frac{1}{3}}=3\times \frac{1}{3}$$

Whakarūnātia. Ko te uara x=\frac{1}{3} kua ngata te whārite.

$$1=1$$

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

$$\sqrt{4-9\left(-\frac{4}{3}\right)}=3\left(-\frac{4}{3}\right)$$

Whakarūnātia. Ko te uara x=-\frac{4}{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 \sqrt{4-9x}=3x he rongoā ahurei.

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