Whakaoti i te sqrt{x+2}+x=10

$$\sqrt{ x+2 } +x=10$$

Whakaoti mō x

$$x=7$$

Ngā Upane Otinga

Me tango x mai i ngā taha e rua o te whārite.

$$\sqrt{x+2}=10-x$$

Pūruatia ngā taha e rua o te whārite.

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

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

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

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(10-x\right)^{2}.

$$x+2=100-20x+x^{2}$$

Tangohia te 100 mai i ngā taha e rua.

$$x+2-100=-20x+x^{2}$$

Tangohia te 100 i te 2, ka -98.

$$x-98=-20x+x^{2}$$

Me tāpiri te 20x ki ngā taha e rua.

$$x-98+20x=x^{2}$$

Pahekotia te x me 20x, ka 21x.

$$21x-98=x^{2}$$

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

$$21x-98-x^{2}=0$$

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

$$-x^{2}+21x-98=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -x^{2}+ax+bx-98. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=21 ab=-\left(-98\right)=98$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōrunga te a+b, he tōrunga hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 98.

$$1,98 2,49 7,14$$

Tātaihia te tapeke mō ia takirua.

$$1+98=99 2+49=51 7+14=21$$

Ko te otinga te takirua ka hoatu i te tapeke 21.

$$a=14 b=7$$

Tuhia anō te -x^{2}+21x-98 hei \left(-x^{2}+14x\right)+\left(7x-98\right).

$$\left(-x^{2}+14x\right)+\left(7x-98\right)$$

Tauwehea te -x i te tuatahi me te 7 i te rōpū tuarua.

$$-x\left(x-14\right)+7\left(x-14\right)$$

Whakatauwehea atu te kīanga pātahi x-14 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-14\right)\left(-x+7\right)$$

Hei kimi otinga whārite, me whakaoti te x-14=0 me te -x+7=0.

$$x=14 x=7$$

Whakakapia te 14 mō te x i te whārite \sqrt{x+2}+x=10.

$$\sqrt{14+2}+14=10$$

Whakarūnātia. Ko te uara x=14 kāore e ngata ana ki te whārite.

$$18=10$$

Whakakapia te 7 mō te x i te whārite \sqrt{x+2}+x=10.

$$\sqrt{7+2}+7=10$$

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

$$10=10$$

Ko te whārite \sqrt{x+2}=10-x he rongoā ahurei.

$$x=7$$