Whakaoti i te sqrt{2x+48}=x

$$\sqrt { 2 x + 48 } = x$$

Whakaoti mō x

$$x=8$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{2x+48}\right)^{2}=x^{2}$$

Tātaihia te \sqrt{2x+48} mā te pū o 2, kia riro ko 2x+48.

$$2x+48=x^{2}$$

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

$$2x+48-x^{2}=0$$

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

$$-x^{2}+2x+48=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -x^{2}+ax+bx+48. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=2 ab=-48=-48$$

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 -48.

$$-1,48 -2,24 -3,16 -4,12 -6,8$$

Tātaihia te tapeke mō ia takirua.

$$-1+48=47 -2+24=22 -3+16=13 -4+12=8 -6+8=2$$

Ko te otinga te takirua ka hoatu i te tapeke 2.

$$a=8 b=-6$$

Tuhia anō te -x^{2}+2x+48 hei \left(-x^{2}+8x\right)+\left(-6x+48\right).

$$\left(-x^{2}+8x\right)+\left(-6x+48\right)$$

Tauwehea te -x i te tuatahi me te -6 i te rōpū tuarua.

$$-x\left(x-8\right)-6\left(x-8\right)$$

Whakatauwehea atu te kīanga pātahi x-8 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-8\right)\left(-x-6\right)$$

Hei kimi otinga whārite, me whakaoti te x-8=0 me te -x-6=0.

$$x=8 x=-6$$

Whakakapia te 8 mō te x i te whārite \sqrt{2x+48}=x.

$$\sqrt{2\times 8+48}=8$$

Whakarūnātia. Ko te uara x=8 kua ngata te whārite.

$$8=8$$

Whakakapia te -6 mō te x i te whārite \sqrt{2x+48}=x.

$$\sqrt{2\left(-6\right)+48}=-6$$

Whakarūnātia. Ko te uara x=-6 kāore e ngata ana ki te whārite nā te mea e rerekē ngā tohu o te taha maui me te taha katau.

$$6=-6$$

Ko te whārite \sqrt{2x+48}=x he rongoā ahurei.

$$x=8$$