Whakaoti i te -2/3t^2+3t=3

$$- \frac { 2 } { 3 } t ^ { 2 } + 3 t = 3$$

Whakaoti mō t

$$t=3$$

$$t = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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.

$$-\frac{2}{3}t^{2}+3t=3$$

Me tango 3 mai i ngā taha e rua o te whārite.

$$-\frac{2}{3}t^{2}+3t-3=3-3$$

Mā te tango i te 3 i a ia ake anō ka toe ko te 0.

$$-\frac{2}{3}t^{2}+3t-3=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -\frac{2}{3} mō a, 3 mō b, me -3 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{-3±\sqrt{3^{2}-4\left(-\frac{2}{3}\right)\left(-3\right)}}{2\left(-\frac{2}{3}\right)}$$

Pūrua 3.

$$t=\frac{-3±\sqrt{9-4\left(-\frac{2}{3}\right)\left(-3\right)}}{2\left(-\frac{2}{3}\right)}$$

Whakareatia -4 ki te -\frac{2}{3}.

$$t=\frac{-3±\sqrt{9+\frac{8}{3}\left(-3\right)}}{2\left(-\frac{2}{3}\right)}$$

Whakareatia \frac{8}{3} ki te -3.

$$t=\frac{-3±\sqrt{9-8}}{2\left(-\frac{2}{3}\right)}$$

Tāpiri 9 ki te -8.

$$t=\frac{-3±\sqrt{1}}{2\left(-\frac{2}{3}\right)}$$

Tuhia te pūtakerua o te 1.

$$t=\frac{-3±1}{2\left(-\frac{2}{3}\right)}$$

Whakareatia 2 ki te -\frac{2}{3}.

$$t=\frac{-3±1}{-\frac{4}{3}}$$

Nā, me whakaoti te whārite t=\frac{-3±1}{-\frac{4}{3}} ina he tāpiri te ±. Tāpiri -3 ki te 1.

$$t=-\frac{2}{-\frac{4}{3}}$$

Whakawehe -2 ki te -\frac{4}{3} mā te whakarea -2 ki te tau huripoki o -\frac{4}{3}.

$$t=\frac{3}{2}$$

Nā, me whakaoti te whārite t=\frac{-3±1}{-\frac{4}{3}} ina he tango te ±. Tango 1 mai i -3.

$$t=-\frac{4}{-\frac{4}{3}}$$

Whakawehe -4 ki te -\frac{4}{3} mā te whakarea -4 ki te tau huripoki o -\frac{4}{3}.

$$t=3$$

Kua oti te whārite te whakatau.

$$t=\frac{3}{2} t=3$$

Ngā Upane mō te Whakaoti i te Pūrua

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.

$$-\frac{2}{3}t^{2}+3t=3$$

Whakawehea ngā taha e rua o te whārite ki te -\frac{2}{3}, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$\frac{-\frac{2}{3}t^{2}+3t}{-\frac{2}{3}}=\frac{3}{-\frac{2}{3}}$$

Mā te whakawehe ki te -\frac{2}{3} ka wetekia te whakareanga ki te -\frac{2}{3}.

$$t^{2}+\frac{3}{-\frac{2}{3}}t=\frac{3}{-\frac{2}{3}}$$

Whakawehe 3 ki te -\frac{2}{3} mā te whakarea 3 ki te tau huripoki o -\frac{2}{3}.

$$t^{2}-\frac{9}{2}t=\frac{3}{-\frac{2}{3}}$$

Whakawehe 3 ki te -\frac{2}{3} mā te whakarea 3 ki te tau huripoki o -\frac{2}{3}.

$$t^{2}-\frac{9}{2}t=-\frac{9}{2}$$

Whakawehea te -\frac{9}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{9}{4}. Nā, tāpiria te pūrua o te -\frac{9}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$t^{2}-\frac{9}{2}t+\left(-\frac{9}{4}\right)^{2}=-\frac{9}{2}+\left(-\frac{9}{4}\right)^{2}$$

Pūruatia -\frac{9}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$t^{2}-\frac{9}{2}t+\frac{81}{16}=-\frac{9}{2}+\frac{81}{16}$$

Tāpiri -\frac{9}{2} ki te \frac{81}{16} 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.

$$t^{2}-\frac{9}{2}t+\frac{81}{16}=\frac{9}{16}$$

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

$$\left(t-\frac{9}{4}\right)^{2}=\frac{9}{16}$$

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

$$\sqrt{\left(t-\frac{9}{4}\right)^{2}}=\sqrt{\frac{9}{16}}$$

Whakarūnātia.

$$t-\frac{9}{4}=\frac{3}{4} t-\frac{9}{4}=-\frac{3}{4}$$

Me tāpiri \frac{9}{4} ki ngā taha e rua o te whārite.

$$t=3 t=\frac{3}{2}$$