Whakaoti i te sqrt{2x-5}+2=x

$$\sqrt { 2 x - 5 } + 2 = x$$

Whakaoti mō x

$$x=3$$

Ngā Upane Otinga

Me tango 2 mai i ngā taha e rua o te whārite.

$$\sqrt{2x-5}=x-2$$

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{2x-5}\right)^{2}=\left(x-2\right)^{2}$$

Tātaihia te \sqrt{2x-5} mā te pū o 2, kia riro ko 2x-5.

$$2x-5=\left(x-2\right)^{2}$$

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

$$2x-5=x^{2}-4x+4$$

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

$$2x-5-x^{2}=-4x+4$$

Me tāpiri te 4x ki ngā taha e rua.

$$2x-5-x^{2}+4x=4$$

Pahekotia te 2x me 4x, ka 6x.

$$6x-5-x^{2}=4$$

Tangohia te 4 mai i ngā taha e rua.

$$6x-5-x^{2}-4=0$$

Tangohia te 4 i te -5, ka -9.

$$6x-9-x^{2}=0$$

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

$$-x^{2}+6x-9=0$$

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.

$$a+b=6 ab=-\left(-9\right)=9$$

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 6.

$$a=3 b=3$$

Tuhia anō te -x^{2}+6x-9 hei \left(-x^{2}+3x\right)+\left(3x-9\right).

$$\left(-x^{2}+3x\right)+\left(3x-9\right)$$

Tauwehea te -x i te tuatahi me te 3 i te rōpū tuarua.

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

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

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

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

$$x=3 x=3$$

Whakakapia te 3 mō te x i te whārite \sqrt{2x-5}+2=x.

$$\sqrt{2\times 3-5}+2=3$$

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

$$3=3$$

Whakakapia te 3 mō te x i te whārite \sqrt{2x-5}+2=x.

$$\sqrt{2\times 3-5}+2=3$$

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

$$3=3$$

Rārangihia ngā rongoā katoa o \sqrt{2x-5}=x-2.

$$x=3 x=3$$