Whakaoti i te sqrt{2x+9}=x+5

$$\sqrt { 2 x + 9 } = x + 5$$

Whakaoti mō x

$$x=-4$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{2x+9}\right)^{2}=\left(x+5\right)^{2}$$

Tātaihia te \sqrt{2x+9} mā te pū o 2, kia riro ko 2x+9.

$$2x+9=\left(x+5\right)^{2}$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+5\right)^{2}.

$$2x+9=x^{2}+10x+25$$

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

$$2x+9-x^{2}=10x+25$$

Tangohia te 10x mai i ngā taha e rua.

$$2x+9-x^{2}-10x=25$$

Pahekotia te 2x me -10x, ka -8x.

$$-8x+9-x^{2}=25$$

Tangohia te 25 mai i ngā taha e rua.

$$-8x+9-x^{2}-25=0$$

Tangohia te 25 i te 9, ka -16.

$$-8x-16-x^{2}=0$$

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

$$-x^{2}-8x-16=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -x^{2}+ax+bx-16. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-8 ab=-\left(-16\right)=16$$

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 16.

$$-1,-16 -2,-8 -4,-4$$

Tātaihia te tapeke mō ia takirua.

$$-1-16=-17 -2-8=-10 -4-4=-8$$

Ko te otinga te takirua ka hoatu i te tapeke -8.

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

Tuhia anō te -x^{2}-8x-16 hei \left(-x^{2}-4x\right)+\left(-4x-16\right).

$$\left(-x^{2}-4x\right)+\left(-4x-16\right)$$

Tauwehea te x i te tuatahi me te 4 i te rōpū tuarua.

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

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

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

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

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

Whakakapia te -4 mō te x i te whārite \sqrt{2x+9}=x+5.

$$\sqrt{2\left(-4\right)+9}=-4+5$$

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

$$1=1$$

Whakakapia te -4 mō te x i te whārite \sqrt{2x+9}=x+5.

$$\sqrt{2\left(-4\right)+9}=-4+5$$

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

$$1=1$$

Rārangihia ngā rongoā katoa o \sqrt{2x+9}=x+5.

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