Whakaoti i te 1+1/n-1=1/n^2-n

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

Whakaoti mō n

$$n=-1$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Tē taea kia ōrite te tāupe n ki tētahi o ngā uara 0,1 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te n\left(n-1\right), arā, te tauraro pātahi he tino iti rawa te kitea o n-1,n^{2}-n.

$$n\left(n-1\right)+n=1$$

Whakamahia te āhuatanga tohatoha hei whakarea te n ki te n-1.

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

Pahekotia te -n me n, ka 0.

$$n^{2}=1$$

Tangohia te 1 mai i ngā taha e rua.

$$n^{2}-1=0$$

Whakaarohia te n^{2}-1. Tuhia anō te n^{2}-1 hei n^{2}-1^{2}. Ka taea te rerekētanga o ngā pūrua te whakatauwehe mā te ture: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(n-1\right)\left(n+1\right)=0$$

Hei kimi otinga whārite, me whakaoti te n-1=0 me te n+1=0.

$$n=1 n=-1$$

Tē taea kia ōrite te tāupe n ki 1.

$$n=-1$$

Ngā Upane mā te Kimi Pūtakerua

Tē taea kia ōrite te tāupe n ki tētahi o ngā uara 0,1 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te n\left(n-1\right), arā, te tauraro pātahi he tino iti rawa te kitea o n-1,n^{2}-n.

$$n\left(n-1\right)+n=1$$

Whakamahia te āhuatanga tohatoha hei whakarea te n ki te n-1.

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

Pahekotia te -n me n, ka 0.

$$n^{2}=1$$

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

$$n=1 n=-1$$

Tē taea kia ōrite te tāupe n ki 1.

$$n=-1$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe n ki tētahi o ngā uara 0,1 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te n\left(n-1\right), arā, te tauraro pātahi he tino iti rawa te kitea o n-1,n^{2}-n.

$$n\left(n-1\right)+n=1$$

Whakamahia te āhuatanga tohatoha hei whakarea te n ki te n-1.

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

Pahekotia te -n me n, ka 0.

$$n^{2}=1$$

Tangohia te 1 mai i ngā taha e rua.

$$n^{2}-1=0$$

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

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

Pūrua 0.

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

Whakareatia -4 ki te -1.

$$n=\frac{0±\sqrt{4}}{2}$$

Tuhia te pūtakerua o te 4.

$$n=\frac{0±2}{2}$$

Nā, me whakaoti te whārite n=\frac{0±2}{2} ina he tāpiri te ±. Whakawehe 2 ki te 2.

$$n=1$$

Nā, me whakaoti te whārite n=\frac{0±2}{2} ina he tango te ±. Whakawehe -2 ki te 2.

$$n=-1$$

Kua oti te whārite te whakatau.

$$n=1 n=-1$$

Tē taea kia ōrite te tāupe n ki 1.

$$n=-1$$