Whakaoti i te 1-n/4=1/n

$$1 - \frac { n } { 4 } = \frac { 1 } { n }$$

Whakaoti mō n

$$n=2$$

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 4n, arā, te tauraro pātahi he tino iti rawa te kitea o 4,n.

$$4n-nn=4$$

Whakareatia te n ki te n, ka n^{2}.

$$4n-n^{2}=4$$

Tangohia te 4 mai i ngā taha e rua.

$$4n-n^{2}-4=0$$

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.

$$-n^{2}+4n-4=0$$

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

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

Pūrua 4.

$$n=\frac{-4±\sqrt{16-4\left(-1\right)\left(-4\right)}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$n=\frac{-4±\sqrt{16+4\left(-4\right)}}{2\left(-1\right)}$$

Whakareatia 4 ki te -4.

$$n=\frac{-4±\sqrt{16-16}}{2\left(-1\right)}$$

Tāpiri 16 ki te -16.

$$n=\frac{-4±\sqrt{0}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 0.

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

Whakareatia 2 ki te -1.

$$n=-\frac{4}{-2}$$

Whakawehe -4 ki te -2.

$$n=2$$

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 4n, arā, te tauraro pātahi he tino iti rawa te kitea o 4,n.

$$4n-nn=4$$

Whakareatia te n ki te n, ka n^{2}.

$$4n-n^{2}=4$$

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.

$$-n^{2}+4n=4$$

Whakawehea ngā taha e rua ki te -1.

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

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

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

Whakawehe 4 ki te -1.

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

Whakawehe 4 ki te -1.

$$n^{2}-4n=-4$$

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

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

Pūrua -2.

$$n^{2}-4n+4=-4+4$$

Tāpiri -4 ki te 4.

$$n^{2}-4n+4=0$$

Tauwehea te n^{2}-4n+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}.

$$\left(n-2\right)^{2}=0$$

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

$$\sqrt{\left(n-2\right)^{2}}=\sqrt{0}$$

Whakarūnātia.

$$n-2=0 n-2=0$$

Me tāpiri 2 ki ngā taha e rua o te whārite.

$$n=2 n=2$$

Kua oti te whārite te whakatau. He ōrite ngā whakatau.

$$n=2$$