Whakaoti i te 10beta*33/(beta*33-045)^2=9*33*2/(33-045)^2

$$\frac { 10 \beta \times 33 } { ( \beta \times 33 - 045 ) ^ { 2 } } = \frac { 9 \times 33 \times 2 } { ( 33 - 045 ) ^ { 2 } }$$

Whakaoti mō β

$$\beta =\frac{5}{9}\approx 0.555555556$$

Ngā Upane Whakamahi Tauwehe

Tē taea kia ōrite te tāupe \beta ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te 1089\beta ^{2}.

$$10\beta \times 33=\beta ^{2}\times 9\times 33\times 2$$

Whakareatia te 10 ki te 33, ka 330.

$$330\beta =\beta ^{2}\times 9\times 33\times 2$$

Whakareatia te 9 ki te 33, ka 297.

$$330\beta =\beta ^{2}\times 297\times 2$$

Whakareatia te 297 ki te 2, ka 594.

$$330\beta =\beta ^{2}\times 594$$

Tangohia te \beta ^{2}\times 594 mai i ngā taha e rua.

$$330\beta -\beta ^{2}\times 594=0$$

Whakareatia te -1 ki te 594, ka -594.

$$330\beta -594\beta ^{2}=0$$

Tauwehea te \beta .

$$\beta \left(330-594\beta \right)=0$$

Hei kimi otinga whārite, me whakaoti te \beta =0 me te 330-594\beta =0.

$$\beta =0 \beta =\frac{5}{9}$$

Tē taea kia ōrite te tāupe \beta ki 0.

$$\beta =\frac{5}{9}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe \beta ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te 1089\beta ^{2}.

$$10\beta \times 33=\beta ^{2}\times 9\times 33\times 2$$

Whakareatia te 10 ki te 33, ka 330.

$$330\beta =\beta ^{2}\times 9\times 33\times 2$$

Whakareatia te 9 ki te 33, ka 297.

$$330\beta =\beta ^{2}\times 297\times 2$$

Whakareatia te 297 ki te 2, ka 594.

$$330\beta =\beta ^{2}\times 594$$

Tangohia te \beta ^{2}\times 594 mai i ngā taha e rua.

$$330\beta -\beta ^{2}\times 594=0$$

Whakareatia te -1 ki te 594, ka -594.

$$330\beta -594\beta ^{2}=0$$

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.

$$-594\beta ^{2}+330\beta =0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -594 mō a, 330 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$\beta =\frac{-330±\sqrt{330^{2}}}{2\left(-594\right)}$$

Tuhia te pūtakerua o te 330^{2}.

$$\beta =\frac{-330±330}{2\left(-594\right)}$$

Whakareatia 2 ki te -594.

$$\beta =\frac{-330±330}{-1188}$$

Nā, me whakaoti te whārite \beta =\frac{-330±330}{-1188} ina he tāpiri te ±. Tāpiri -330 ki te 330.

$$\beta =\frac{0}{-1188}$$

Whakawehe 0 ki te -1188.

$$\beta =0$$

Nā, me whakaoti te whārite \beta =\frac{-330±330}{-1188} ina he tango te ±. Tango 330 mai i -330.

$$\beta =-\frac{660}{-1188}$$

Whakahekea te hautanga \frac{-660}{-1188} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 132.

$$\beta =\frac{5}{9}$$

Kua oti te whārite te whakatau.

$$\beta =0 \beta =\frac{5}{9}$$

Tē taea kia ōrite te tāupe \beta ki 0.

$$\beta =\frac{5}{9}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe \beta ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te 1089\beta ^{2}.

$$10\beta \times 33=\beta ^{2}\times 9\times 33\times 2$$

Whakareatia te 10 ki te 33, ka 330.

$$330\beta =\beta ^{2}\times 9\times 33\times 2$$

Whakareatia te 9 ki te 33, ka 297.

$$330\beta =\beta ^{2}\times 297\times 2$$

Whakareatia te 297 ki te 2, ka 594.

$$330\beta =\beta ^{2}\times 594$$

Tangohia te \beta ^{2}\times 594 mai i ngā taha e rua.

$$330\beta -\beta ^{2}\times 594=0$$

Whakareatia te -1 ki te 594, ka -594.

$$330\beta -594\beta ^{2}=0$$

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.

$$-594\beta ^{2}+330\beta =0$$

Whakawehea ngā taha e rua ki te -594.

$$\frac{-594\beta ^{2}+330\beta }{-594}=\frac{0}{-594}$$

Mā te whakawehe ki te -594 ka wetekia te whakareanga ki te -594.

$$\beta ^{2}+\frac{330}{-594}\beta =\frac{0}{-594}$$

Whakahekea te hautanga \frac{330}{-594} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 66.

$$\beta ^{2}-\frac{5}{9}\beta =\frac{0}{-594}$$

Whakawehe 0 ki te -594.

$$\beta ^{2}-\frac{5}{9}\beta =0$$

Whakawehea te -\frac{5}{9}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{5}{18}. Nā, tāpiria te pūrua o te -\frac{5}{18} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$\beta ^{2}-\frac{5}{9}\beta +\left(-\frac{5}{18}\right)^{2}=\left(-\frac{5}{18}\right)^{2}$$

Pūruatia -\frac{5}{18} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$\beta ^{2}-\frac{5}{9}\beta +\frac{25}{324}=\frac{25}{324}$$

Tauwehea \beta ^{2}-\frac{5}{9}\beta +\frac{25}{324}. 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}.

$$\left(\beta -\frac{5}{18}\right)^{2}=\frac{25}{324}$$

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

$$\sqrt{\left(\beta -\frac{5}{18}\right)^{2}}=\sqrt{\frac{25}{324}}$$

Whakarūnātia.

$$\beta -\frac{5}{18}=\frac{5}{18} \beta -\frac{5}{18}=-\frac{5}{18}$$

Me tāpiri \frac{5}{18} ki ngā taha e rua o te whārite.

$$\beta =\frac{5}{9} \beta =0$$

Tē taea kia ōrite te tāupe \beta ki 0.

$$\beta =\frac{5}{9}$$