Whakaoti i te sqrt{2x+35}=x

$$\sqrt { 2 x + 35 } = x$$

Whakaoti mō x

$$x=7$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{2x+35}\right)^{2}=x^{2}$$

Tātaihia te \sqrt{2x+35} mā te pū o 2, kia riro ko 2x+35.

$$2x+35=x^{2}$$

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

$$2x+35-x^{2}=0$$

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

$$-x^{2}+2x+35=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -x^{2}+ax+bx+35. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=2 ab=-35=-35$$

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 -35.

$$-1,35 -5,7$$

Tātaihia te tapeke mō ia takirua.

$$-1+35=34 -5+7=2$$

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

$$a=7 b=-5$$

Tuhia anō te -x^{2}+2x+35 hei \left(-x^{2}+7x\right)+\left(-5x+35\right).

$$\left(-x^{2}+7x\right)+\left(-5x+35\right)$$

Tauwehea te -x i te tuatahi me te -5 i te rōpū tuarua.

$$-x\left(x-7\right)-5\left(x-7\right)$$

Whakatauwehea atu te kīanga pātahi x-7 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-7\right)\left(-x-5\right)$$

Hei kimi otinga whārite, me whakaoti te x-7=0 me te -x-5=0.

$$x=7 x=-5$$

Whakakapia te 7 mō te x i te whārite \sqrt{2x+35}=x.

$$\sqrt{2\times 7+35}=7$$

Whakarūnātia. Ko te uara x=7 kua ngata te whārite.

$$7=7$$

Whakakapia te -5 mō te x i te whārite \sqrt{2x+35}=x.

$$\sqrt{2\left(-5\right)+35}=-5$$

Whakarūnātia. Ko te uara x=-5 kāore e ngata ana ki te whārite nā te mea e rerekē ngā tohu o te taha maui me te taha katau.

$$5=-5$$

Ko te whārite \sqrt{2x+35}=x he rongoā ahurei.

$$x=7$$