Whakaoti i te sqrt{3x+10}=x+4

$$\sqrt{ 3x+10 } = x+4$$

Whakaoti mō x

$$x=-2$$

$$x=-3$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{3x+10}\right)^{2}=\left(x+4\right)^{2}$$

Tātaihia te \sqrt{3x+10} mā te pū o 2, kia riro ko 3x+10.

$$3x+10=\left(x+4\right)^{2}$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+4\right)^{2}.

$$3x+10=x^{2}+8x+16$$

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

$$3x+10-x^{2}=8x+16$$

Tangohia te 8x mai i ngā taha e rua.

$$3x+10-x^{2}-8x=16$$

Pahekotia te 3x me -8x, ka -5x.

$$-5x+10-x^{2}=16$$

Tangohia te 16 mai i ngā taha e rua.

$$-5x+10-x^{2}-16=0$$

Tangohia te 16 i te 10, ka -6.

$$-5x-6-x^{2}=0$$

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

$$-x^{2}-5x-6=0$$

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.

$$a+b=-5 ab=-\left(-6\right)=6$$

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 6.

$$-1,-6 -2,-3$$

Tātaihia te tapeke mō ia takirua.

$$-1-6=-7 -2-3=-5$$

Ko te otinga te takirua ka hoatu i te tapeke -5.

$$a=-2 b=-3$$

Tuhia anō te -x^{2}-5x-6 hei \left(-x^{2}-2x\right)+\left(-3x-6\right).

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

Tauwehea te x i te tuatahi me te 3 i te rōpū tuarua.

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

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

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

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

$$x=-2 x=-3$$

Whakakapia te -2 mō te x i te whārite \sqrt{3x+10}=x+4.

$$\sqrt{3\left(-2\right)+10}=-2+4$$

Whakarūnātia. Ko te uara x=-2 kua ngata te whārite.

$$2=2$$

Whakakapia te -3 mō te x i te whārite \sqrt{3x+10}=x+4.

$$\sqrt{3\left(-3\right)+10}=-3+4$$

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

$$1=1$$

Rārangihia ngā rongoā katoa o \sqrt{3x+10}=x+4.

$$x=-2 x=-3$$