Whakaoti i te 3y^2-2/5=y

$$\frac { 3 y ^ { 2 } - 2 } { 5 } = y$$

Whakaoti mō y

$$y=-\frac{1}{3}\approx -0.333333333$$

$$y=2$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakawehea ia wā o 3y^{2}-2 ki te 5, kia riro ko \frac{3}{5}y^{2}-\frac{2}{5}.

$$\frac{3}{5}y^{2}-\frac{2}{5}=y$$

Tangohia te y mai i ngā taha e rua.

$$\frac{3}{5}y^{2}-\frac{2}{5}-y=0$$

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.

$$\frac{3}{5}y^{2}-y-\frac{2}{5}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi \frac{3}{5} mō a, -1 mō b, me -\frac{2}{5} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{-\left(-1\right)±\sqrt{1-4\times \frac{3}{5}\left(-\frac{2}{5}\right)}}{2\times \frac{3}{5}}$$

Whakareatia -4 ki te \frac{3}{5}.

$$y=\frac{-\left(-1\right)±\sqrt{1-\frac{12}{5}\left(-\frac{2}{5}\right)}}{2\times \frac{3}{5}}$$

Whakareatia -\frac{12}{5} ki te -\frac{2}{5} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$y=\frac{-\left(-1\right)±\sqrt{1+\frac{24}{25}}}{2\times \frac{3}{5}}$$

Tāpiri 1 ki te \frac{24}{25}.

$$y=\frac{-\left(-1\right)±\sqrt{\frac{49}{25}}}{2\times \frac{3}{5}}$$

Tuhia te pūtakerua o te \frac{49}{25}.

$$y=\frac{-\left(-1\right)±\frac{7}{5}}{2\times \frac{3}{5}}$$

Ko te tauaro o -1 ko 1.

$$y=\frac{1±\frac{7}{5}}{2\times \frac{3}{5}}$$

Whakareatia 2 ki te \frac{3}{5}.

$$y=\frac{1±\frac{7}{5}}{\frac{6}{5}}$$

Nā, me whakaoti te whārite y=\frac{1±\frac{7}{5}}{\frac{6}{5}} ina he tāpiri te ±. Tāpiri 1 ki te \frac{7}{5}.

$$y=\frac{\frac{12}{5}}{\frac{6}{5}}$$

Whakawehe \frac{12}{5} ki te \frac{6}{5} mā te whakarea \frac{12}{5} ki te tau huripoki o \frac{6}{5}.

$$y=2$$

Nā, me whakaoti te whārite y=\frac{1±\frac{7}{5}}{\frac{6}{5}} ina he tango te ±. Tango \frac{7}{5} mai i 1.

$$y=-\frac{\frac{2}{5}}{\frac{6}{5}}$$

Whakawehe -\frac{2}{5} ki te \frac{6}{5} mā te whakarea -\frac{2}{5} ki te tau huripoki o \frac{6}{5}.

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

Kua oti te whārite te whakatau.

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

Ngā Upane mō te Whakaoti i te Pūrua

Whakawehea ia wā o 3y^{2}-2 ki te 5, kia riro ko \frac{3}{5}y^{2}-\frac{2}{5}.

$$\frac{3}{5}y^{2}-\frac{2}{5}=y$$

Tangohia te y mai i ngā taha e rua.

$$\frac{3}{5}y^{2}-\frac{2}{5}-y=0$$

Me tāpiri te \frac{2}{5} ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$\frac{3}{5}y^{2}-y=\frac{2}{5}$$

Whakawehea ngā taha e rua o te whārite ki te \frac{3}{5}, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$\frac{\frac{3}{5}y^{2}-y}{\frac{3}{5}}=\frac{\frac{2}{5}}{\frac{3}{5}}$$

Mā te whakawehe ki te \frac{3}{5} ka wetekia te whakareanga ki te \frac{3}{5}.

$$y^{2}+\left(-\frac{1}{\frac{3}{5}}\right)y=\frac{\frac{2}{5}}{\frac{3}{5}}$$

Whakawehe -1 ki te \frac{3}{5} mā te whakarea -1 ki te tau huripoki o \frac{3}{5}.

$$y^{2}-\frac{5}{3}y=\frac{\frac{2}{5}}{\frac{3}{5}}$$

Whakawehe \frac{2}{5} ki te \frac{3}{5} mā te whakarea \frac{2}{5} ki te tau huripoki o \frac{3}{5}.

$$y^{2}-\frac{5}{3}y=\frac{2}{3}$$

Whakawehea te -\frac{5}{3}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{5}{6}. Nā, tāpiria te pūrua o te -\frac{5}{6} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$y^{2}-\frac{5}{3}y+\left(-\frac{5}{6}\right)^{2}=\frac{2}{3}+\left(-\frac{5}{6}\right)^{2}$$

Pūruatia -\frac{5}{6} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$y^{2}-\frac{5}{3}y+\frac{25}{36}=\frac{2}{3}+\frac{25}{36}$$

Tāpiri \frac{2}{3} ki te \frac{25}{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.

$$y^{2}-\frac{5}{3}y+\frac{25}{36}=\frac{49}{36}$$

Tauwehea y^{2}-\frac{5}{3}y+\frac{25}{36}. 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}.

$$\left(y-\frac{5}{6}\right)^{2}=\frac{49}{36}$$

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

$$\sqrt{\left(y-\frac{5}{6}\right)^{2}}=\sqrt{\frac{49}{36}}$$

Whakarūnātia.

$$y-\frac{5}{6}=\frac{7}{6} y-\frac{5}{6}=-\frac{7}{6}$$

Me tāpiri \frac{5}{6} ki ngā taha e rua o te whārite.

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