Whakaoti i te sqrt{3x+28}=x+8

$$\sqrt{ 3x+28 } = x+8$$

Whakaoti mō x

$$x=-4$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{3x+28}\right)^{2}=\left(x+8\right)^{2}$$

Tātaihia te \sqrt{3x+28} mā te pū o 2, kia riro ko 3x+28.

$$3x+28=\left(x+8\right)^{2}$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+8\right)^{2}.

$$3x+28=x^{2}+16x+64$$

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

$$3x+28-x^{2}=16x+64$$

Tangohia te 16x mai i ngā taha e rua.

$$3x+28-x^{2}-16x=64$$

Pahekotia te 3x me -16x, ka -13x.

$$-13x+28-x^{2}=64$$

Tangohia te 64 mai i ngā taha e rua.

$$-13x+28-x^{2}-64=0$$

Tangohia te 64 i te 28, ka -36.

$$-13x-36-x^{2}=0$$

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

$$-x^{2}-13x-36=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -x^{2}+ax+bx-36. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-13 ab=-\left(-36\right)=36$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōraro te a+b, he tōraro hoki a a me b. 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.

$$-1-36=-37 -2-18=-20 -3-12=-15 -4-9=-13 -6-6=-12$$

Ko te otinga te takirua ka hoatu i te tapeke -13.

$$a=-4 b=-9$$

Tuhia anō te -x^{2}-13x-36 hei \left(-x^{2}-4x\right)+\left(-9x-36\right).

$$\left(-x^{2}-4x\right)+\left(-9x-36\right)$$

Tauwehea te x i te tuatahi me te 9 i te rōpū tuarua.

$$x\left(-x-4\right)+9\left(-x-4\right)$$

Whakatauwehea atu te kīanga pātahi -x-4 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(-x-4\right)\left(x+9\right)$$

Hei kimi otinga whārite, me whakaoti te -x-4=0 me te x+9=0.

$$x=-4 x=-9$$

Whakakapia te -4 mō te x i te whārite \sqrt{3x+28}=x+8.

$$\sqrt{3\left(-4\right)+28}=-4+8$$

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

$$4=4$$

Whakakapia te -9 mō te x i te whārite \sqrt{3x+28}=x+8.

$$\sqrt{3\left(-9\right)+28}=-9+8$$

Whakarūnātia. Ko te uara x=-9 kāore e ngata ana ki te whārite nā te mea e rerekē ngā tohu o te taha maui me te taha katau.

$$1=-1$$

Ko te whārite \sqrt{3x+28}=x+8 he rongoā ahurei.

$$x=-4$$