Whakaoti i te a-3=sqrt{a+3}

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

Whakaoti mō a

$$a=6$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

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

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

$$a^{2}-6a+9=\left(\sqrt{a+3}\right)^{2}$$

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

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

Tangohia te a mai i ngā taha e rua.

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

Pahekotia te -6a me -a, ka -7a.

$$a^{2}-7a+9=3$$

Tangohia te 3 mai i ngā taha e rua.

$$a^{2}-7a+9-3=0$$

Tangohia te 3 i te 9, ka 6.

$$a^{2}-7a+6=0$$

Hei whakaoti i te whārite, whakatauwehea te a^{2}-7a+6 mā te whakamahi i te tātai a^{2}+\left(a+b\right)a+ab=\left(a+a\right)\left(a+b\right). Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-7 ab=6$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōraro te a+b, he tōraro 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 -7.

$$a=-6 b=-1$$

Me tuhi anō te kīanga whakatauwehe \left(a+a\right)\left(a+b\right) mā ngā uara i tātaihia.

$$\left(a-6\right)\left(a-1\right)$$

Hei kimi otinga whārite, me whakaoti te a-6=0 me te a-1=0.

$$a=6 a=1$$

Whakakapia te 6 mō te a i te whārite a-3=\sqrt{a+3}.

$$6-3=\sqrt{6+3}$$

Whakarūnātia. Ko te uara a=6 kua ngata te whārite.

$$3=3$$

Whakakapia te 1 mō te a i te whārite a-3=\sqrt{a+3}.

$$1-3=\sqrt{1+3}$$

Whakarūnātia. Ko te uara a=1 kāore e ngata ana ki te whārite nā te mea e rerekē ngā tohu o te taha maui me te taha katau.

$$-2=2$$

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

$$a=6$$