Whakaoti i te x-6sqrt{x+1}+10=0

$$x-6 \sqrt{ x+1 } +10=0$$

Whakaoti mō x

$$x=8$$

Ngā Upane Otinga

Tangohia te 10 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$x-6\sqrt{x+1}=-10$$

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

$$-6\sqrt{x+1}=-10-x$$

Pūruatia ngā taha e rua o te whārite.

$$\left(-6\sqrt{x+1}\right)^{2}=\left(-10-x\right)^{2}$$

Whakarohaina te \left(-6\sqrt{x+1}\right)^{2}.

$$\left(-6\right)^{2}\left(\sqrt{x+1}\right)^{2}=\left(-10-x\right)^{2}$$

Tātaihia te -6 mā te pū o 2, kia riro ko 36.

$$36\left(\sqrt{x+1}\right)^{2}=\left(-10-x\right)^{2}$$

Tātaihia te \sqrt{x+1} mā te pū o 2, kia riro ko x+1.

$$36\left(x+1\right)=\left(-10-x\right)^{2}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 36 ki te x+1.

$$36x+36=\left(-10-x\right)^{2}$$

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

$$36x+36=100+20x+x^{2}$$

Tangohia te 20x mai i ngā taha e rua.

$$36x+36-20x=100+x^{2}$$

Pahekotia te 36x me -20x, ka 16x.

$$16x+36=100+x^{2}$$

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

$$16x+36-x^{2}=100$$

Tangohia te 100 mai i ngā taha e rua.

$$16x+36-x^{2}-100=0$$

Tangohia te 100 i te 36, ka -64.

$$16x-64-x^{2}=0$$

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

$$-x^{2}+16x-64=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -x^{2}+ax+bx-64. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=16 ab=-\left(-64\right)=64$$

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 64.

$$1,64 2,32 4,16 8,8$$

Tātaihia te tapeke mō ia takirua.

$$1+64=65 2+32=34 4+16=20 8+8=16$$

Ko te otinga te takirua ka hoatu i te tapeke 16.

$$a=8 b=8$$

Tuhia anō te -x^{2}+16x-64 hei \left(-x^{2}+8x\right)+\left(8x-64\right).

$$\left(-x^{2}+8x\right)+\left(8x-64\right)$$

Tauwehea te -x i te tuatahi me te 8 i te rōpū tuarua.

$$-x\left(x-8\right)+8\left(x-8\right)$$

Whakatauwehea atu te kīanga pātahi x-8 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-8\right)\left(-x+8\right)$$

Hei kimi otinga whārite, me whakaoti te x-8=0 me te -x+8=0.

$$x=8 x=8$$

Whakakapia te 8 mō te x i te whārite x-6\sqrt{x+1}+10=0.

$$8-6\sqrt{8+1}+10=0$$

Whakarūnātia. Ko te uara x=8 kua ngata te whārite.

$$0=0$$

Whakakapia te 8 mō te x i te whārite x-6\sqrt{x+1}+10=0.

$$8-6\sqrt{8+1}+10=0$$

Whakarūnātia. Ko te uara x=8 kua ngata te whārite.

$$0=0$$

Rārangihia ngā rongoā katoa o -6\sqrt{x+1}=-x-10.

$$x=8 x=8$$