Whakaoti i te 3/n^3=n-4/3n^2+2/3n^2

$$\frac{ 3 }{ { n }^{ 3 } } = \frac{ n-4 }{ 3 { n }^{ 2 } } + \frac{ 2 }{ 3 { n }^{ 2 } }$$

Whakaoti mō n

$$n=\sqrt{10}+1\approx 4.16227766$$

$$n=1-\sqrt{10}\approx -2.16227766$$

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 3n^{3}, arā, te tauraro pātahi he tino iti rawa te kitea o n^{3},3n^{2}.

$$3\times 3=n\left(n-4\right)+n\times 2$$

Whakareatia te 3 ki te 3, ka 9.

$$9=n\left(n-4\right)+n\times 2$$

Whakamahia te āhuatanga tohatoha hei whakarea te n ki te n-4.

$$9=n^{2}-4n+n\times 2$$

Pahekotia te -4n me n\times 2, ka -2n.

$$9=n^{2}-2n$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$n^{2}-2n=9$$

Tangohia te 9 mai i ngā taha e rua.

$$n^{2}-2n-9=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -2 mō b, me -9 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Pūrua -2.

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

Whakareatia -4 ki te -9.

$$n=\frac{-\left(-2\right)±\sqrt{4+36}}{2}$$

Tāpiri 4 ki te 36.

$$n=\frac{-\left(-2\right)±\sqrt{40}}{2}$$

Tuhia te pūtakerua o te 40.

$$n=\frac{-\left(-2\right)±2\sqrt{10}}{2}$$

Ko te tauaro o -2 ko 2.

$$n=\frac{2±2\sqrt{10}}{2}$$

Nā, me whakaoti te whārite n=\frac{2±2\sqrt{10}}{2} ina he tāpiri te ±. Tāpiri 2 ki te 2\sqrt{10}.

$$n=\frac{2\sqrt{10}+2}{2}$$

Whakawehe 2+2\sqrt{10} ki te 2.

$$n=\sqrt{10}+1$$

Nā, me whakaoti te whārite n=\frac{2±2\sqrt{10}}{2} ina he tango te ±. Tango 2\sqrt{10} mai i 2.

$$n=\frac{2-2\sqrt{10}}{2}$$

Whakawehe 2-2\sqrt{10} ki te 2.

$$n=1-\sqrt{10}$$

Kua oti te whārite te whakatau.

$$n=\sqrt{10}+1 n=1-\sqrt{10}$$

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 3n^{3}, arā, te tauraro pātahi he tino iti rawa te kitea o n^{3},3n^{2}.

$$3\times 3=n\left(n-4\right)+n\times 2$$

Whakareatia te 3 ki te 3, ka 9.

$$9=n\left(n-4\right)+n\times 2$$

Whakamahia te āhuatanga tohatoha hei whakarea te n ki te n-4.

$$9=n^{2}-4n+n\times 2$$

Pahekotia te -4n me n\times 2, ka -2n.

$$9=n^{2}-2n$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$n^{2}-2n=9$$

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

$$n^{2}-2n+1=9+1$$

Tāpiri 9 ki te 1.

$$n^{2}-2n+1=10$$

Tauwehea te n^{2}-2n+1. 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}.

$$\left(n-1\right)^{2}=10$$

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

$$\sqrt{\left(n-1\right)^{2}}=\sqrt{10}$$

Whakarūnātia.

$$n-1=\sqrt{10} n-1=-\sqrt{10}$$

Me tāpiri 1 ki ngā taha e rua o te whārite.

$$n=\sqrt{10}+1 n=1-\sqrt{10}$$