Whakaoti i te (y+2)^2=25

$$( y + 2 ) ^ { 2 } = 25$$

Whakaoti mō y

$$y=3$$

$$y=-7$$

Ngā Upane Whakamahi Tauwehe

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

$$y^{2}+4y+4=25$$

Tangohia te 25 mai i ngā taha e rua.

$$y^{2}+4y+4-25=0$$

Tangohia te 25 i te 4, ka -21.

$$y^{2}+4y-21=0$$

Hei whakaoti i te whārite, whakatauwehea te y^{2}+4y-21 mā te whakamahi i te tātai y^{2}+\left(a+b\right)y+ab=\left(y+a\right)\left(y+b\right). Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=4 ab=-21$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -21.

$$-1,21 -3,7$$

Tātaihia te tapeke mō ia takirua.

$$-1+21=20 -3+7=4$$

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

$$a=-3 b=7$$

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

$$\left(y-3\right)\left(y+7\right)$$

Hei kimi otinga whārite, me whakaoti te y-3=0 me te y+7=0.

$$y=3 y=-7$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

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

$$y^{2}+4y+4=25$$

Tangohia te 25 mai i ngā taha e rua.

$$y^{2}+4y+4-25=0$$

Tangohia te 25 i te 4, ka -21.

$$y^{2}+4y-21=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei y^{2}+ay+by-21. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=4 ab=1\left(-21\right)=-21$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -21.

$$-1,21 -3,7$$

Tātaihia te tapeke mō ia takirua.

$$-1+21=20 -3+7=4$$

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

$$a=-3 b=7$$

Tuhia anō te y^{2}+4y-21 hei \left(y^{2}-3y\right)+\left(7y-21\right).

$$\left(y^{2}-3y\right)+\left(7y-21\right)$$

Tauwehea te y i te tuatahi me te 7 i te rōpū tuarua.

$$y\left(y-3\right)+7\left(y-3\right)$$

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

$$\left(y-3\right)\left(y+7\right)$$

Hei kimi otinga whārite, me whakaoti te y-3=0 me te y+7=0.

$$y=3 y=-7$$

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(y+2\right)^{2}.

$$y^{2}+4y+4=25$$

Tangohia te 25 mai i ngā taha e rua.

$$y^{2}+4y+4-25=0$$

Tangohia te 25 i te 4, ka -21.

$$y^{2}+4y-21=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 4 mō b, me -21 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{-4±\sqrt{4^{2}-4\left(-21\right)}}{2}$$

Pūrua 4.

$$y=\frac{-4±\sqrt{16-4\left(-21\right)}}{2}$$

Whakareatia -4 ki te -21.

$$y=\frac{-4±\sqrt{16+84}}{2}$$

Tāpiri 16 ki te 84.

$$y=\frac{-4±\sqrt{100}}{2}$$

Tuhia te pūtakerua o te 100.

$$y=\frac{-4±10}{2}$$

Nā, me whakaoti te whārite y=\frac{-4±10}{2} ina he tāpiri te ±. Tāpiri -4 ki te 10.

$$y=\frac{6}{2}$$

Whakawehe 6 ki te 2.

$$y=3$$

Nā, me whakaoti te whārite y=\frac{-4±10}{2} ina he tango te ±. Tango 10 mai i -4.

$$y=-\frac{14}{2}$$

Whakawehe -14 ki te 2.

$$y=-7$$

Kua oti te whārite te whakatau.

$$y=3 y=-7$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$\sqrt{\left(y+2\right)^{2}}=\sqrt{25}$$

Whakarūnātia.

$$y+2=5 y+2=-5$$

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

$$y=3 y=-7$$