Whakaoti i te sqrt{a-4}+1=sqrt{2a-7}

$$\sqrt { a - 4 } + 1 = \sqrt { 2 a - 7 }$$

Whakaoti mō a

$$a=8$$

$$a=4$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{a-4}+1\right)^{2}=\left(\sqrt{2a-7}\right)^{2}$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(\sqrt{a-4}+1\right)^{2}.

$$\left(\sqrt{a-4}\right)^{2}+2\sqrt{a-4}+1=\left(\sqrt{2a-7}\right)^{2}$$

Tātaihia te \sqrt{a-4} mā te pū o 2, kia riro ko a-4.

$$a-4+2\sqrt{a-4}+1=\left(\sqrt{2a-7}\right)^{2}$$

Tāpirihia te -4 ki te 1, ka -3.

$$a-3+2\sqrt{a-4}=\left(\sqrt{2a-7}\right)^{2}$$

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

$$a-3+2\sqrt{a-4}=2a-7$$

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

$$2\sqrt{a-4}=2a-7-\left(a-3\right)$$

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

$$2\sqrt{a-4}=2a-7-a+3$$

Pahekotia te 2a me -a, ka a.

$$2\sqrt{a-4}=a-7+3$$

Tāpirihia te -7 ki te 3, ka -4.

$$2\sqrt{a-4}=a-4$$

Pūruatia ngā taha e rua o te whārite.

$$\left(2\sqrt{a-4}\right)^{2}=\left(a-4\right)^{2}$$

Whakarohaina te \left(2\sqrt{a-4}\right)^{2}.

$$2^{2}\left(\sqrt{a-4}\right)^{2}=\left(a-4\right)^{2}$$

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

$$4\left(\sqrt{a-4}\right)^{2}=\left(a-4\right)^{2}$$

Tātaihia te \sqrt{a-4} mā te pū o 2, kia riro ko a-4.

$$4\left(a-4\right)=\left(a-4\right)^{2}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te a-4.

$$4a-16=\left(a-4\right)^{2}$$

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

$$4a-16=a^{2}-8a+16$$

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

$$4a-16-a^{2}=-8a+16$$

Me tāpiri te 8a ki ngā taha e rua.

$$4a-16-a^{2}+8a=16$$

Pahekotia te 4a me 8a, ka 12a.

$$12a-16-a^{2}=16$$

Tangohia te 16 mai i ngā taha e rua.

$$12a-16-a^{2}-16=0$$

Tangohia te 16 i te -16, ka -32.

$$12a-32-a^{2}=0$$

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

$$-a^{2}+12a-32=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -a^{2}+aa+ba-32. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=12 ab=-\left(-32\right)=32$$

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 32.

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

Tātaihia te tapeke mō ia takirua.

$$1+32=33 2+16=18 4+8=12$$

Ko te otinga te takirua ka hoatu i te tapeke 12.

$$a=8 b=4$$

Tuhia anō te -a^{2}+12a-32 hei \left(-a^{2}+8a\right)+\left(4a-32\right).

$$\left(-a^{2}+8a\right)+\left(4a-32\right)$$

Tauwehea te -a i te tuatahi me te 4 i te rōpū tuarua.

$$-a\left(a-8\right)+4\left(a-8\right)$$

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

$$\left(a-8\right)\left(-a+4\right)$$

Hei kimi otinga whārite, me whakaoti te a-8=0 me te -a+4=0.

$$a=8 a=4$$

Whakakapia te 8 mō te a i te whārite \sqrt{a-4}+1=\sqrt{2a-7}.

$$\sqrt{8-4}+1=\sqrt{2\times 8-7}$$

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

$$3=3$$

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

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

Whakarūnātia. Ko te uara a=4 kua ngata te whārite.

$$1=1$$

Rārangihia ngā rongoā katoa o \sqrt{a-4}+1=\sqrt{2a-7}.

$$a=8 a=4$$