Whakaoti i te sqrt{3x^2+7x-4}=-x

$$\sqrt{ 3 { x }^{ 2 } +7x-4 } = -x$$

Whakaoti mō x

$$x=-4$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{3x^{2}+7x-4}\right)^{2}=\left(-x\right)^{2}$$

Tātaihia te \sqrt{3x^{2}+7x-4} mā te pū o 2, kia riro ko 3x^{2}+7x-4.

$$3x^{2}+7x-4=\left(-x\right)^{2}$$

Tātaihia te -x mā te pū o 2, kia riro ko x^{2}.

$$3x^{2}+7x-4=x^{2}$$

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

$$3x^{2}+7x-4-x^{2}=0$$

Pahekotia te 3x^{2} me -x^{2}, ka 2x^{2}.

$$2x^{2}+7x-4=0$$

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

$$a+b=7 ab=2\left(-4\right)=-8$$

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 -8.

$$-1,8 -2,4$$

Tātaihia te tapeke mō ia takirua.

$$-1+8=7 -2+4=2$$

Ko te otinga te takirua ka hoatu i te tapeke 7.

$$a=-1 b=8$$

Tuhia anō te 2x^{2}+7x-4 hei \left(2x^{2}-x\right)+\left(8x-4\right).

$$\left(2x^{2}-x\right)+\left(8x-4\right)$$

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

$$x\left(2x-1\right)+4\left(2x-1\right)$$

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

$$\left(2x-1\right)\left(x+4\right)$$

Hei kimi otinga whārite, me whakaoti te 2x-1=0 me te x+4=0.

$$x=\frac{1}{2} x=-4$$

Whakakapia te \frac{1}{2} mō te x i te whārite \sqrt{3x^{2}+7x-4}=-x.

$$\sqrt{3\times \left(\frac{1}{2}\right)^{2}+7\times \frac{1}{2}-4}=-\frac{1}{2}$$

Whakarūnātia. Ko te uara x=\frac{1}{2} kāore e ngata ana ki te whārite nā te mea e rerekē ngā tohu o te taha maui me te taha katau.

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

Whakakapia te -4 mō te x i te whārite \sqrt{3x^{2}+7x-4}=-x.

$$\sqrt{3\left(-4\right)^{2}+7\left(-4\right)-4}=-\left(-4\right)$$

Whakarūnātia. Ko te uara x=-4 kua ngata te whārite.

$$4=4$$

Ko te whārite \sqrt{3x^{2}+7x-4}=-x he rongoā ahurei.

$$x=-4$$