Whakaoti i te y^2=9y+14

$$y ^ { 2 } = 9 y + 14$$

Whakaoti mō y

$$y = \frac{\sqrt{137} + 9}{2} \approx 10.352349955$$

$$y=\frac{9-\sqrt{137}}{2}\approx -1.352349955$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 9y mai i ngā taha e rua.

$$y^{2}-9y=14$$

Tangohia te 14 mai i ngā taha e rua.

$$y^{2}-9y-14=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -9 mō b, me -14 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}-4\left(-14\right)}}{2}$$

Pūrua -9.

$$y=\frac{-\left(-9\right)±\sqrt{81-4\left(-14\right)}}{2}$$

Whakareatia -4 ki te -14.

$$y=\frac{-\left(-9\right)±\sqrt{81+56}}{2}$$

Tāpiri 81 ki te 56.

$$y=\frac{-\left(-9\right)±\sqrt{137}}{2}$$

Ko te tauaro o -9 ko 9.

$$y=\frac{9±\sqrt{137}}{2}$$

Nā, me whakaoti te whārite y=\frac{9±\sqrt{137}}{2} ina he tāpiri te ±. Tāpiri 9 ki te \sqrt{137}.

$$y=\frac{\sqrt{137}+9}{2}$$

Nā, me whakaoti te whārite y=\frac{9±\sqrt{137}}{2} ina he tango te ±. Tango \sqrt{137} mai i 9.

$$y=\frac{9-\sqrt{137}}{2}$$

Kua oti te whārite te whakatau.

$$y=\frac{\sqrt{137}+9}{2} y=\frac{9-\sqrt{137}}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 9y mai i ngā taha e rua.

$$y^{2}-9y=14$$

Whakawehea te -9, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{9}{2}. Nā, tāpiria te pūrua o te -\frac{9}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$y^{2}-9y+\left(-\frac{9}{2}\right)^{2}=14+\left(-\frac{9}{2}\right)^{2}$$

Pūruatia -\frac{9}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$y^{2}-9y+\frac{81}{4}=14+\frac{81}{4}$$

Tāpiri 14 ki te \frac{81}{4}.

$$y^{2}-9y+\frac{81}{4}=\frac{137}{4}$$

Tauwehea y^{2}-9y+\frac{81}{4}. 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}.

$$\left(y-\frac{9}{2}\right)^{2}=\frac{137}{4}$$

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

$$\sqrt{\left(y-\frac{9}{2}\right)^{2}}=\sqrt{\frac{137}{4}}$$

Whakarūnātia.

$$y-\frac{9}{2}=\frac{\sqrt{137}}{2} y-\frac{9}{2}=-\frac{\sqrt{137}}{2}$$

Me tāpiri \frac{9}{2} ki ngā taha e rua o te whārite.

$$y=\frac{\sqrt{137}+9}{2} y=\frac{9-\sqrt{137}}{2}$$