Whakaoti i te 32n/24n=4n^2/3n

$$\frac { 32 n } { 24 n } = \frac { 4 n ^ { 2 } } { 3 n }$$

Whakaoti mō n

$$n=1$$

Ngā Upane Whakamahi Tauwehe

Tē taea kia ōrite te tāupe n ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 24n, arā, te tauraro pātahi he tino iti rawa te kitea o 24n,3n.

$$32n=8\times 4n^{2}$$

Whakareatia te 8 ki te 4, ka 32.

$$32n=32n^{2}$$

Tangohia te 32n^{2} mai i ngā taha e rua.

$$32n-32n^{2}=0$$

Tauwehea te n.

$$n\left(32-32n\right)=0$$

Hei kimi otinga whārite, me whakaoti te n=0 me te 32-32n=0.

$$n=0 n=1$$

Tē taea kia ōrite te tāupe n ki 0.

$$n=1$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe n ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 24n, arā, te tauraro pātahi he tino iti rawa te kitea o 24n,3n.

$$32n=8\times 4n^{2}$$

Whakareatia te 8 ki te 4, ka 32.

$$32n=32n^{2}$$

Tangohia te 32n^{2} mai i ngā taha e rua.

$$32n-32n^{2}=0$$

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.

$$-32n^{2}+32n=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -32 mō a, 32 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{-32±\sqrt{32^{2}}}{2\left(-32\right)}$$

Tuhia te pūtakerua o te 32^{2}.

$$n=\frac{-32±32}{2\left(-32\right)}$$

Whakareatia 2 ki te -32.

$$n=\frac{-32±32}{-64}$$

Nā, me whakaoti te whārite n=\frac{-32±32}{-64} ina he tāpiri te ±. Tāpiri -32 ki te 32.

$$n=\frac{0}{-64}$$

Whakawehe 0 ki te -64.

$$n=0$$

Nā, me whakaoti te whārite n=\frac{-32±32}{-64} ina he tango te ±. Tango 32 mai i -32.

$$n=-\frac{64}{-64}$$

Whakawehe -64 ki te -64.

$$n=1$$

Kua oti te whārite te whakatau.

$$n=0 n=1$$

Tē taea kia ōrite te tāupe n ki 0.

$$n=1$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe n ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 24n, arā, te tauraro pātahi he tino iti rawa te kitea o 24n,3n.

$$32n=8\times 4n^{2}$$

Whakareatia te 8 ki te 4, ka 32.

$$32n=32n^{2}$$

Tangohia te 32n^{2} mai i ngā taha e rua.

$$32n-32n^{2}=0$$

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.

$$-32n^{2}+32n=0$$

Whakawehea ngā taha e rua ki te -32.

$$\frac{-32n^{2}+32n}{-32}=\frac{0}{-32}$$

Mā te whakawehe ki te -32 ka wetekia te whakareanga ki te -32.

$$n^{2}+\frac{32}{-32}n=\frac{0}{-32}$$

Whakawehe 32 ki te -32.

$$n^{2}-n=\frac{0}{-32}$$

Whakawehe 0 ki te -32.

$$n^{2}-n=0$$

Whakawehea te -1, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{1}{2}. Nā, tāpiria te pūrua o te -\frac{1}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$n^{2}-n+\left(-\frac{1}{2}\right)^{2}=\left(-\frac{1}{2}\right)^{2}$$

Pūruatia -\frac{1}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$n^{2}-n+\frac{1}{4}=\frac{1}{4}$$

Tauwehea te n^{2}-n+\frac{1}{4}. Ko te tikanga, ina ko x^{2}+bx+c he pūrua tika, ka taea te tauwehe i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(n-\frac{1}{2}\right)^{2}=\frac{1}{4}$$

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

$$\sqrt{\left(n-\frac{1}{2}\right)^{2}}=\sqrt{\frac{1}{4}}$$

Whakarūnātia.

$$n-\frac{1}{2}=\frac{1}{2} n-\frac{1}{2}=-\frac{1}{2}$$

Me tāpiri \frac{1}{2} ki ngā taha e rua o te whārite.

$$n=1 n=0$$

Tē taea kia ōrite te tāupe n ki 0.

$$n=1$$