Whakaoti i te sqrt{3-x}-x+3=0

$$\sqrt { 3 - x } - x + 3 = 0$$

Whakaoti mō x

$$x=3$$

Ngā Upane Otinga

Me tango -x+3 mai i ngā taha e rua o te whārite.

$$\sqrt{3-x}=-\left(-x+3\right)$$

Hei kimi i te tauaro o -x+3, kimihia te tauaro o ia taurangi.

$$\sqrt{3-x}=-\left(-x\right)-3$$

Ko te tauaro o -x ko x.

$$\sqrt{3-x}=x-3$$

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{3-x}\right)^{2}=\left(x-3\right)^{2}$$

Tātaihia te \sqrt{3-x} mā te pū o 2, kia riro ko 3-x.

$$3-x=\left(x-3\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-3\right)^{2}.

$$3-x=x^{2}-6x+9$$

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

$$3-x-x^{2}=-6x+9$$

Me tāpiri te 6x ki ngā taha e rua.

$$3-x-x^{2}+6x=9$$

Pahekotia te -x me 6x, ka 5x.

$$3+5x-x^{2}=9$$

Tangohia te 9 mai i ngā taha e rua.

$$3+5x-x^{2}-9=0$$

Tangohia te 9 i te 3, ka -6.

$$-6+5x-x^{2}=0$$

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

$$-x^{2}+5x-6=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -x^{2}+ax+bx-6. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=5 ab=-\left(-6\right)=6$$

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 6.

$$1,6 2,3$$

Tātaihia te tapeke mō ia takirua.

$$1+6=7 2+3=5$$

Ko te otinga te takirua ka hoatu i te tapeke 5.

$$a=3 b=2$$

Tuhia anō te -x^{2}+5x-6 hei \left(-x^{2}+3x\right)+\left(2x-6\right).

$$\left(-x^{2}+3x\right)+\left(2x-6\right)$$

Tauwehea te -x i te tuatahi me te 2 i te rōpū tuarua.

$$-x\left(x-3\right)+2\left(x-3\right)$$

Whakatauwehea atu te kīanga pātahi x-3 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-3\right)\left(-x+2\right)$$

Hei kimi otinga whārite, me whakaoti te x-3=0 me te -x+2=0.

$$x=3 x=2$$

Whakakapia te 3 mō te x i te whārite \sqrt{3-x}-x+3=0.

$$\sqrt{3-3}-3+3=0$$

Whakarūnātia. Ko te uara x=3 kua ngata te whārite.

$$0=0$$

Whakakapia te 2 mō te x i te whārite \sqrt{3-x}-x+3=0.

$$\sqrt{3-2}-2+3=0$$

Whakarūnātia. Ko te uara x=2 kāore e ngata ana ki te whārite.

$$2=0$$

Ko te whārite \sqrt{3-x}=x-3 he rongoā ahurei.

$$x=3$$