Whakaoti i te a-sqrt{a}=6

$$a- \sqrt{ a } =6$$

Whakaoti mō a

$$a=9$$

Ngā Upane Otinga

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

$$-\sqrt{a}=6-a$$

Pūruatia ngā taha e rua o te whārite.

$$\left(-\sqrt{a}\right)^{2}=\left(6-a\right)^{2}$$

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

$$\left(-1\right)^{2}\left(\sqrt{a}\right)^{2}=\left(6-a\right)^{2}$$

Tātaihia te -1 mā te pū o 2, kia riro ko 1.

$$1\left(\sqrt{a}\right)^{2}=\left(6-a\right)^{2}$$

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

$$1a=\left(6-a\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(6-a\right)^{2}.

$$1a=36-12a+a^{2}$$

Whakaraupapatia anō ngā kīanga tau.

$$a=a^{2}-12a+36$$

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

$$a-a^{2}=-12a+36$$

Me tāpiri te 12a ki ngā taha e rua.

$$a-a^{2}+12a=36$$

Pahekotia te a me 12a, ka 13a.

$$13a-a^{2}=36$$

Tangohia te 36 mai i ngā taha e rua.

$$13a-a^{2}-36=0$$

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

$$-a^{2}+13a-36=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -a^{2}+aa+ba-36. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=13 ab=-\left(-36\right)=36$$

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 36.

$$1,36 2,18 3,12 4,9 6,6$$

Tātaihia te tapeke mō ia takirua.

$$1+36=37 2+18=20 3+12=15 4+9=13 6+6=12$$

Ko te otinga te takirua ka hoatu i te tapeke 13.

$$a=9 b=4$$

Tuhia anō te -a^{2}+13a-36 hei \left(-a^{2}+9a\right)+\left(4a-36\right).

$$\left(-a^{2}+9a\right)+\left(4a-36\right)$$

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

$$-a\left(a-9\right)+4\left(a-9\right)$$

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

$$\left(a-9\right)\left(-a+4\right)$$

Hei kimi otinga whārite, me whakaoti te a-9=0 me te -a+4=0.

$$a=9 a=4$$

Whakakapia te 9 mō te a i te whārite a-\sqrt{a}=6.

$$9-\sqrt{9}=6$$

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

$$6=6$$

Whakakapia te 4 mō te a i te whārite a-\sqrt{a}=6.

$$4-\sqrt{4}=6$$

Whakarūnātia. Ko te uara a=4 kāore e ngata ana ki te whārite.

$$2=6$$

Ko te whārite -\sqrt{a}=6-a he rongoā ahurei.

$$a=9$$