Whakaoti i te 1/1-x^2=1

$$\frac { 1 } { 1 - x ^ { 2 } } = 1$$

Whakaoti mō x

$$x=0$$

Ngā Upane mā te Kimi Pūtakerua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -1,1 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te \left(x-1\right)\left(-x-1\right).

$$1=\left(x-1\right)\left(-x-1\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x-1 ki te -x-1 ka whakakotahi i ngā kupu rite.

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

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

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

Tangohia te 1 mai i ngā taha e rua.

$$-x^{2}=1-1$$

Tangohia te 1 i te 1, ka 0.

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

Whakawehea ngā taha e rua ki te -1. Ko te kore i whakawehea ki te tau ehara te kore ka hua ko te kore.

$$x^{2}=0$$

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

$$x=0 x=0$$

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

$$x=0$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -1,1 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te \left(x-1\right)\left(-x-1\right).

$$1=\left(x-1\right)\left(-x-1\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x-1 ki te -x-1 ka whakakotahi i ngā kupu rite.

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

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

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

Tangohia te 1 mai i ngā taha e rua.

$$-x^{2}+1-1=0$$

Tangohia te 1 i te 1, ka 0.

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

Whakawehea ngā taha e rua ki te -1. Ko te kore i whakawehea ki te tau ehara te kore ka hua ko te kore.

$$x^{2}=0$$

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

$$x=\frac{0±\sqrt{0^{2}}}{2}$$

Tuhia te pūtakerua o te 0^{2}.

$$x=\frac{0±0}{2}$$

Whakawehe 0 ki te 2.

$$x=0$$