Whakaoti i te (13/2-y)*y=-12

$$( \frac { 13 } { 2 } - y ) \cdot y = - 12$$

Whakaoti mō y

$$y=8$$

$$y = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{13}{2}-y ki te y.

$$\frac{13}{2}y-y^{2}=-12$$

Me tāpiri te 12 ki ngā taha e rua.

$$\frac{13}{2}y-y^{2}+12=0$$

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$-y^{2}+\frac{13}{2}y+12=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, \frac{13}{2} mō b, me 12 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{-\frac{13}{2}±\sqrt{\left(\frac{13}{2}\right)^{2}-4\left(-1\right)\times 12}}{2\left(-1\right)}$$

Pūruatia \frac{13}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$y=\frac{-\frac{13}{2}±\sqrt{\frac{169}{4}-4\left(-1\right)\times 12}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$y=\frac{-\frac{13}{2}±\sqrt{\frac{169}{4}+4\times 12}}{2\left(-1\right)}$$

Whakareatia 4 ki te 12.

$$y=\frac{-\frac{13}{2}±\sqrt{\frac{169}{4}+48}}{2\left(-1\right)}$$

Tāpiri \frac{169}{4} ki te 48.

$$y=\frac{-\frac{13}{2}±\sqrt{\frac{361}{4}}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te \frac{361}{4}.

$$y=\frac{-\frac{13}{2}±\frac{19}{2}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$y=\frac{-\frac{13}{2}±\frac{19}{2}}{-2}$$

Nā, me whakaoti te whārite y=\frac{-\frac{13}{2}±\frac{19}{2}}{-2} ina he tāpiri te ±. Tāpiri -\frac{13}{2} ki te \frac{19}{2} 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.

$$y=\frac{3}{-2}$$

Whakawehe 3 ki te -2.

$$y=-\frac{3}{2}$$

Nā, me whakaoti te whārite y=\frac{-\frac{13}{2}±\frac{19}{2}}{-2} ina he tango te ±. Tango \frac{19}{2} mai i -\frac{13}{2} mā te kimi i te tauraro pātahi me te tango i ngā taurunga, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$y=-\frac{16}{-2}$$

Whakawehe -16 ki te -2.

$$y=8$$

Kua oti te whārite te whakatau.

$$y=-\frac{3}{2} y=8$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{13}{2}-y ki te y.

$$\frac{13}{2}y-y^{2}=-12$$

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$-y^{2}+\frac{13}{2}y=-12$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-y^{2}+\frac{13}{2}y}{-1}=-\frac{12}{-1}$$

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

$$y^{2}+\frac{\frac{13}{2}}{-1}y=-\frac{12}{-1}$$

Whakawehe \frac{13}{2} ki te -1.

$$y^{2}-\frac{13}{2}y=-\frac{12}{-1}$$

Whakawehe -12 ki te -1.

$$y^{2}-\frac{13}{2}y=12$$

Whakawehea te -\frac{13}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{13}{4}. Nā, tāpiria te pūrua o te -\frac{13}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$y^{2}-\frac{13}{2}y+\left(-\frac{13}{4}\right)^{2}=12+\left(-\frac{13}{4}\right)^{2}$$

Pūruatia -\frac{13}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$y^{2}-\frac{13}{2}y+\frac{169}{16}=12+\frac{169}{16}$$

Tāpiri 12 ki te \frac{169}{16}.

$$y^{2}-\frac{13}{2}y+\frac{169}{16}=\frac{361}{16}$$

Tauwehea y^{2}-\frac{13}{2}y+\frac{169}{16}. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(y-\frac{13}{4}\right)^{2}=\frac{361}{16}$$

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

$$\sqrt{\left(y-\frac{13}{4}\right)^{2}}=\sqrt{\frac{361}{16}}$$

Whakarūnātia.

$$y-\frac{13}{4}=\frac{19}{4} y-\frac{13}{4}=-\frac{19}{4}$$

Me tāpiri \frac{13}{4} ki ngā taha e rua o te whārite.

$$y=8 y=-\frac{3}{2}$$