Whakaoti i te (a-2)^2=16

$$( a - 2 ) ^ { 2 } = 16$$

Whakaoti mō a

$$a=6$$

$$a=-2$$

Ngā Upane Whakamahi Tauwehe

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

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

Tangohia te 16 mai i ngā taha e rua.

$$a^{2}-4a+4-16=0$$

Tangohia te 16 i te 4, ka -12.

$$a^{2}-4a-12=0$$

Hei whakaoti i te whārite, whakatauwehea te a^{2}-4a-12 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.

$$a+b=-4 ab=-12$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōraro te a+b, he nui ake te uara pū o te tau tōraro i tō te tōrunga. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -12.

$$1,-12 2,-6 3,-4$$

Tātaihia te tapeke mō ia takirua.

$$1-12=-11 2-6=-4 3-4=-1$$

Ko te otinga te takirua ka hoatu i te tapeke -4.

$$a=-6 b=2$$

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

$$\left(a-6\right)\left(a+2\right)$$

Hei kimi otinga whārite, me whakaoti te a-6=0 me te a+2=0.

$$a=6 a=-2$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

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

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

Tangohia te 16 mai i ngā taha e rua.

$$a^{2}-4a+4-16=0$$

Tangohia te 16 i te 4, ka -12.

$$a^{2}-4a-12=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei a^{2}+aa+ba-12. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-4 ab=1\left(-12\right)=-12$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōraro te a+b, he nui ake te uara pū o te tau tōraro i tō te tōrunga. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -12.

$$1,-12 2,-6 3,-4$$

Tātaihia te tapeke mō ia takirua.

$$1-12=-11 2-6=-4 3-4=-1$$

Ko te otinga te takirua ka hoatu i te tapeke -4.

$$a=-6 b=2$$

Tuhia anō te a^{2}-4a-12 hei \left(a^{2}-6a\right)+\left(2a-12\right).

$$\left(a^{2}-6a\right)+\left(2a-12\right)$$

Tauwehea te a i te tuatahi me te 2 i te rōpū tuarua.

$$a\left(a-6\right)+2\left(a-6\right)$$

Whakatauwehea atu te kīanga pātahi a-6 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(a-6\right)\left(a+2\right)$$

Hei kimi otinga whārite, me whakaoti te a-6=0 me te a+2=0.

$$a=6 a=-2$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

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

Tangohia te 16 mai i ngā taha e rua.

$$a^{2}-4a+4-16=0$$

Tangohia te 16 i te 4, ka -12.

$$a^{2}-4a-12=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -4 mō b, me -12 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\left(-12\right)}}{2}$$

Pūrua -4.

$$a=\frac{-\left(-4\right)±\sqrt{16-4\left(-12\right)}}{2}$$

Whakareatia -4 ki te -12.

$$a=\frac{-\left(-4\right)±\sqrt{16+48}}{2}$$

Tāpiri 16 ki te 48.

$$a=\frac{-\left(-4\right)±\sqrt{64}}{2}$$

Tuhia te pūtakerua o te 64.

$$a=\frac{-\left(-4\right)±8}{2}$$

Ko te tauaro o -4 ko 4.

$$a=\frac{4±8}{2}$$

Nā, me whakaoti te whārite a=\frac{4±8}{2} ina he tāpiri te ±. Tāpiri 4 ki te 8.

$$a=\frac{12}{2}$$

Whakawehe 12 ki te 2.

$$a=6$$

Nā, me whakaoti te whārite a=\frac{4±8}{2} ina he tango te ±. Tango 8 mai i 4.

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

Whakawehe -4 ki te 2.

$$a=-2$$

Kua oti te whārite te whakatau.

$$a=6 a=-2$$

Ngā Upane mō te Whakaoti i te Pūrua

Tuhia te pūtakerua o ngā taha e rua o te whārite.

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

Whakarūnātia.

$$a-2=4 a-2=-4$$

Me tāpiri 2 ki ngā taha e rua o te whārite.

$$a=6 a=-2$$