Whakaoti i te sqrt{2x+7}+4=x

$$\sqrt { 2 x + 7 } + 4 = x$$

Whakaoti mō x

$$x=9$$

Ngā Upane Otinga

Me tango 4 mai i ngā taha e rua o te whārite.

$$\sqrt{2x+7}=x-4$$

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{2x+7}\right)^{2}=\left(x-4\right)^{2}$$

Tātaihia te \sqrt{2x+7} mā te pū o 2, kia riro ko 2x+7.

$$2x+7=\left(x-4\right)^{2}$$

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

$$2x+7=x^{2}-8x+16$$

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

$$2x+7-x^{2}=-8x+16$$

Me tāpiri te 8x ki ngā taha e rua.

$$2x+7-x^{2}+8x=16$$

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

$$10x+7-x^{2}=16$$

Tangohia te 16 mai i ngā taha e rua.

$$10x+7-x^{2}-16=0$$

Tangohia te 16 i te 7, ka -9.

$$10x-9-x^{2}=0$$

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

$$-x^{2}+10x-9=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -x^{2}+ax+bx-9. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=10 ab=-\left(-9\right)=9$$

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 9.

$$1,9 3,3$$

Tātaihia te tapeke mō ia takirua.

$$1+9=10 3+3=6$$

Ko te otinga te takirua ka hoatu i te tapeke 10.

$$a=9 b=1$$

Tuhia anō te -x^{2}+10x-9 hei \left(-x^{2}+9x\right)+\left(x-9\right).

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

Whakatauwehea atu -x i te -x^{2}+9x.

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

Whakatauwehea atu te kīanga pātahi x-9 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-9\right)\left(-x+1\right)$$

Hei kimi otinga whārite, me whakaoti te x-9=0 me te -x+1=0.

$$x=9 x=1$$

Whakakapia te 9 mō te x i te whārite \sqrt{2x+7}+4=x.

$$\sqrt{2\times 9+7}+4=9$$

Whakarūnātia. Ko te uara x=9 kua ngata te whārite.

$$9=9$$

Whakakapia te 1 mō te x i te whārite \sqrt{2x+7}+4=x.

$$\sqrt{2\times 1+7}+4=1$$

Whakarūnātia. Ko te uara x=1 kāore e ngata ana ki te whārite.

$$7=1$$

Ko te whārite \sqrt{2x+7}=x-4 he rongoā ahurei.

$$x=9$$