Whakaoti i te 8+sqrt{36x}=2x

$$8+ \sqrt{ 36x } =2x$$

Whakaoti mō x

$$x=16$$

Ngā Upane Otinga

Me tango 8 mai i ngā taha e rua o te whārite.

$$\sqrt{36x}=2x-8$$

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{36x}\right)^{2}=\left(2x-8\right)^{2}$$

Tātaihia te \sqrt{36x} mā te pū o 2, kia riro ko 36x.

$$36x=\left(2x-8\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(2x-8\right)^{2}.

$$36x=4x^{2}-32x+64$$

Tangohia te 4x^{2} mai i ngā taha e rua.

$$36x-4x^{2}=-32x+64$$

Me tāpiri te 32x ki ngā taha e rua.

$$36x-4x^{2}+32x=64$$

Pahekotia te 36x me 32x, ka 68x.

$$68x-4x^{2}=64$$

Tangohia te 64 mai i ngā taha e rua.

$$68x-4x^{2}-64=0$$

Whakawehea ngā taha e rua ki te 4.

$$17x-x^{2}-16=0$$

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

$$-x^{2}+17x-16=0$$

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.

$$a+b=17 ab=-\left(-16\right)=16$$

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 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 17.

$$a=16 b=1$$

Tuhia anō te -x^{2}+17x-16 hei \left(-x^{2}+16x\right)+\left(x-16\right).

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

Whakatauwehea atu -x i te -x^{2}+16x.

$$-x\left(x-16\right)+x-16$$

Whakatauwehea atu te kīanga pātahi x-16 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-16\right)\left(-x+1\right)$$

Hei kimi otinga whārite, me whakaoti te x-16=0 me te -x+1=0.

$$x=16 x=1$$

Whakakapia te 16 mō te x i te whārite 8+\sqrt{36x}=2x.

$$8+\sqrt{36\times 16}=2\times 16$$

Whakarūnātia. Ko te uara x=16 kua ngata te whārite.

$$32=32$$

Whakakapia te 1 mō te x i te whārite 8+\sqrt{36x}=2x.

$$8+\sqrt{36\times 1}=2\times 1$$

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

$$14=2$$

Ko te whārite \sqrt{36x}=2x-8 he rongoā ahurei.

$$x=16$$