Whakaoti i te 36y=12+18:(-27y)

$$36 y = 12 + 18 : ( - 27 y )$$

Whakaoti mō y

$$y=\frac{\sqrt{3}}{18}+\frac{1}{6}\approx 0.262891712$$

$$y=-\frac{\sqrt{3}}{18}+\frac{1}{6}\approx 0.070441622$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe y ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te -27y.

$$36y\left(-27\right)y=-27y\times 12+18$$

Whakareatia te 36 ki te -27, ka -972.

$$-972yy=-27y\times 12+18$$

Whakareatia te y ki te y, ka y^{2}.

$$-972y^{2}=-27y\times 12+18$$

Whakareatia te -27 ki te 12, ka -324.

$$-972y^{2}=-324y+18$$

Me tāpiri te 324y ki ngā taha e rua.

$$-972y^{2}+324y=18$$

Tangohia te 18 mai i ngā taha e rua.

$$-972y^{2}+324y-18=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -972 mō a, 324 mō b, me -18 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{-324±\sqrt{324^{2}-4\left(-972\right)\left(-18\right)}}{2\left(-972\right)}$$

Pūrua 324.

$$y=\frac{-324±\sqrt{104976-4\left(-972\right)\left(-18\right)}}{2\left(-972\right)}$$

Whakareatia -4 ki te -972.

$$y=\frac{-324±\sqrt{104976+3888\left(-18\right)}}{2\left(-972\right)}$$

Whakareatia 3888 ki te -18.

$$y=\frac{-324±\sqrt{104976-69984}}{2\left(-972\right)}$$

Tāpiri 104976 ki te -69984.

$$y=\frac{-324±\sqrt{34992}}{2\left(-972\right)}$$

Tuhia te pūtakerua o te 34992.

$$y=\frac{-324±108\sqrt{3}}{2\left(-972\right)}$$

Whakareatia 2 ki te -972.

$$y=\frac{-324±108\sqrt{3}}{-1944}$$

Nā, me whakaoti te whārite y=\frac{-324±108\sqrt{3}}{-1944} ina he tāpiri te ±. Tāpiri -324 ki te 108\sqrt{3}.

$$y=\frac{108\sqrt{3}-324}{-1944}$$

Whakawehe -324+108\sqrt{3} ki te -1944.

$$y=-\frac{\sqrt{3}}{18}+\frac{1}{6}$$

Nā, me whakaoti te whārite y=\frac{-324±108\sqrt{3}}{-1944} ina he tango te ±. Tango 108\sqrt{3} mai i -324.

$$y=\frac{-108\sqrt{3}-324}{-1944}$$

Whakawehe -324-108\sqrt{3} ki te -1944.

$$y=\frac{\sqrt{3}}{18}+\frac{1}{6}$$

Kua oti te whārite te whakatau.

$$y=-\frac{\sqrt{3}}{18}+\frac{1}{6} y=\frac{\sqrt{3}}{18}+\frac{1}{6}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe y ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te -27y.

$$36y\left(-27\right)y=-27y\times 12+18$$

Whakareatia te 36 ki te -27, ka -972.

$$-972yy=-27y\times 12+18$$

Whakareatia te y ki te y, ka y^{2}.

$$-972y^{2}=-27y\times 12+18$$

Whakareatia te -27 ki te 12, ka -324.

$$-972y^{2}=-324y+18$$

Me tāpiri te 324y ki ngā taha e rua.

$$-972y^{2}+324y=18$$

Whakawehea ngā taha e rua ki te -972.

$$\frac{-972y^{2}+324y}{-972}=\frac{18}{-972}$$

Mā te whakawehe ki te -972 ka wetekia te whakareanga ki te -972.

$$y^{2}+\frac{324}{-972}y=\frac{18}{-972}$$

Whakahekea te hautanga \frac{324}{-972} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 324.

$$y^{2}-\frac{1}{3}y=\frac{18}{-972}$$

Whakahekea te hautanga \frac{18}{-972} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 18.

$$y^{2}-\frac{1}{3}y=-\frac{1}{54}$$

Whakawehea te -\frac{1}{3}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{1}{6}. Nā, tāpiria te pūrua o te -\frac{1}{6} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$y^{2}-\frac{1}{3}y+\left(-\frac{1}{6}\right)^{2}=-\frac{1}{54}+\left(-\frac{1}{6}\right)^{2}$$

Pūruatia -\frac{1}{6} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$y^{2}-\frac{1}{3}y+\frac{1}{36}=-\frac{1}{54}+\frac{1}{36}$$

Tāpiri -\frac{1}{54} ki te \frac{1}{36} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$y^{2}-\frac{1}{3}y+\frac{1}{36}=\frac{1}{108}$$

Tauwehea te y^{2}-\frac{1}{3}y+\frac{1}{36}. 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}.

$$\left(y-\frac{1}{6}\right)^{2}=\frac{1}{108}$$

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

$$\sqrt{\left(y-\frac{1}{6}\right)^{2}}=\sqrt{\frac{1}{108}}$$

Whakarūnātia.

$$y-\frac{1}{6}=\frac{\sqrt{3}}{18} y-\frac{1}{6}=-\frac{\sqrt{3}}{18}$$

Me tāpiri \frac{1}{6} ki ngā taha e rua o te whārite.

$$y=\frac{\sqrt{3}}{18}+\frac{1}{6} y=-\frac{\sqrt{3}}{18}+\frac{1}{6}$$