Whakaoti i te 2x=sqrt{4x+24}

$$2 x = \sqrt { 4 x + 24 }$$

Whakaoti mō x

$$x=3$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(2x\right)^{2}=\left(\sqrt{4x+24}\right)^{2}$$

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

$$2^{2}x^{2}=\left(\sqrt{4x+24}\right)^{2}$$

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

$$4x^{2}=\left(\sqrt{4x+24}\right)^{2}$$

Tātaihia te \sqrt{4x+24} mā te pū o 2, kia riro ko 4x+24.

$$4x^{2}=4x+24$$

Tangohia te 4x mai i ngā taha e rua.

$$4x^{2}-4x=24$$

Tangohia te 24 mai i ngā taha e rua.

$$4x^{2}-4x-24=0$$

Whakawehea ngā taha e rua ki te 4.

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

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei x^{2}+ax+bx-6. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

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

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 x^{2}-x-6 hei \left(x^{2}-3x\right)+\left(2x-6\right).

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

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

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

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

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

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

$$x=3 x=-2$$

Whakakapia te 3 mō te x i te whārite 2x=\sqrt{4x+24}.

$$2\times 3=\sqrt{4\times 3+24}$$

Whakarūnātia. Ko te uara x=3 kua ngata te whārite.

$$6=6$$

Whakakapia te -2 mō te x i te whārite 2x=\sqrt{4x+24}.

$$2\left(-2\right)=\sqrt{4\left(-2\right)+24}$$

Whakarūnātia. Ko te uara x=-2 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 2x=\sqrt{4x+24} he rongoā ahurei.

$$x=3$$