Whakaoti i te 72=8/(y-3)^2

$$72 = \frac { 8 } { ( y - 3 ) ^ { 2 } }$$

Whakaoti mō y

$$y = \frac{8}{3} = 2\frac{2}{3} \approx 2.666666667$$

$$y = \frac{10}{3} = 3\frac{1}{3} \approx 3.333333333$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe y ki 3 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te \left(y-3\right)^{2}.

$$72\left(y-3\right)^{2}=8$$

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

$$72\left(y^{2}-6y+9\right)=8$$

Whakamahia te āhuatanga tohatoha hei whakarea te 72 ki te y^{2}-6y+9.

$$72y^{2}-432y+648=8$$

Tangohia te 8 mai i ngā taha e rua.

$$72y^{2}-432y+648-8=0$$

Tangohia te 8 i te 648, ka 640.

$$72y^{2}-432y+640=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 72 mō a, -432 mō b, me 640 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{-\left(-432\right)±\sqrt{\left(-432\right)^{2}-4\times 72\times 640}}{2\times 72}$$

Pūrua -432.

$$y=\frac{-\left(-432\right)±\sqrt{186624-4\times 72\times 640}}{2\times 72}$$

Whakareatia -4 ki te 72.

$$y=\frac{-\left(-432\right)±\sqrt{186624-288\times 640}}{2\times 72}$$

Whakareatia -288 ki te 640.

$$y=\frac{-\left(-432\right)±\sqrt{186624-184320}}{2\times 72}$$

Tāpiri 186624 ki te -184320.

$$y=\frac{-\left(-432\right)±\sqrt{2304}}{2\times 72}$$

Tuhia te pūtakerua o te 2304.

$$y=\frac{-\left(-432\right)±48}{2\times 72}$$

Ko te tauaro o -432 ko 432.

$$y=\frac{432±48}{2\times 72}$$

Whakareatia 2 ki te 72.

$$y=\frac{432±48}{144}$$

Nā, me whakaoti te whārite y=\frac{432±48}{144} ina he tāpiri te ±. Tāpiri 432 ki te 48.

$$y=\frac{480}{144}$$

Whakahekea te hautanga \frac{480}{144} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 48.

$$y=\frac{10}{3}$$

Nā, me whakaoti te whārite y=\frac{432±48}{144} ina he tango te ±. Tango 48 mai i 432.

$$y=\frac{384}{144}$$

Whakahekea te hautanga \frac{384}{144} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 48.

$$y=\frac{8}{3}$$

Kua oti te whārite te whakatau.

$$y=\frac{10}{3} y=\frac{8}{3}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe y ki 3 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te \left(y-3\right)^{2}.

$$72\left(y-3\right)^{2}=8$$

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

$$72\left(y^{2}-6y+9\right)=8$$

Whakamahia te āhuatanga tohatoha hei whakarea te 72 ki te y^{2}-6y+9.

$$72y^{2}-432y+648=8$$

Tangohia te 648 mai i ngā taha e rua.

$$72y^{2}-432y=8-648$$

Tangohia te 648 i te 8, ka -640.

$$72y^{2}-432y=-640$$

Whakawehea ngā taha e rua ki te 72.

$$\frac{72y^{2}-432y}{72}=-\frac{640}{72}$$

Mā te whakawehe ki te 72 ka wetekia te whakareanga ki te 72.

$$y^{2}+\left(-\frac{432}{72}\right)y=-\frac{640}{72}$$

Whakawehe -432 ki te 72.

$$y^{2}-6y=-\frac{640}{72}$$

Whakahekea te hautanga \frac{-640}{72} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 8.

$$y^{2}-6y=-\frac{80}{9}$$

Whakawehea te -6, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -3. Nā, tāpiria te pūrua o te -3 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$y^{2}-6y+\left(-3\right)^{2}=-\frac{80}{9}+\left(-3\right)^{2}$$

Pūrua -3.

$$y^{2}-6y+9=-\frac{80}{9}+9$$

Tāpiri -\frac{80}{9} ki te 9.

$$y^{2}-6y+9=\frac{1}{9}$$

Tauwehea te y^{2}-6y+9. Ko te tikanga, ina ko x^{2}+bx+c he pūrua tika, ka taea te tauwehe i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(y-3\right)^{2}=\frac{1}{9}$$

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

$$\sqrt{\left(y-3\right)^{2}}=\sqrt{\frac{1}{9}}$$

Whakarūnātia.

$$y-3=\frac{1}{3} y-3=-\frac{1}{3}$$

Me tāpiri 3 ki ngā taha e rua o te whārite.

$$y=\frac{10}{3} y=\frac{8}{3}$$