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

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

Whakaoti mō x

$$x=0$$

$$x=2$$

Ngā Upane Whakamahi Tauwehe

Tē taea kia ōrite te tāupe x ki 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)^{2}.

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

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-1\right)^{2}.

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

Whakamahia te āhuatanga tohatoha hei whakarea te -2 ki te x^{2}-2x+1.

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

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

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

Me tāpiri te 2 ki ngā taha e rua.

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

Tāpirihia te -2 ki te 2, ka 0.

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

Tauwehea te x.

$$x\left(-2x+4\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te -2x+4=0.

$$x=0 x=2$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki 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)^{2}.

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

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-1\right)^{2}.

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

Whakamahia te āhuatanga tohatoha hei whakarea te -2 ki te x^{2}-2x+1.

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

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

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

Me tāpiri te 2 ki ngā taha e rua.

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

Tāpirihia te -2 ki te 2, ka 0.

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

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

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

Tuhia te pūtakerua o te 4^{2}.

$$x=\frac{-4±4}{2\left(-2\right)}$$

Whakareatia 2 ki te -2.

$$x=\frac{-4±4}{-4}$$

Nā, me whakaoti te whārite x=\frac{-4±4}{-4} ina he tāpiri te ±. Tāpiri -4 ki te 4.

$$x=\frac{0}{-4}$$

Whakawehe 0 ki te -4.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-4±4}{-4} ina he tango te ±. Tango 4 mai i -4.

$$x=-\frac{8}{-4}$$

Whakawehe -8 ki te -4.

$$x=2$$

Kua oti te whārite te whakatau.

$$x=0 x=2$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki 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)^{2}.

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

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-1\right)^{2}.

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

Whakamahia te āhuatanga tohatoha hei whakarea te -2 ki te x^{2}-2x+1.

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

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

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

Me tāpiri te 2 ki ngā taha e rua.

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

Tāpirihia te -2 ki te 2, ka 0.

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

Whakawehea ngā taha e rua ki te -2.

$$\frac{-2x^{2}+4x}{-2}=\frac{0}{-2}$$

Mā te whakawehe ki te -2 ka wetekia te whakareanga ki te -2.

$$x^{2}+\frac{4}{-2}x=\frac{0}{-2}$$

Whakawehe 4 ki te -2.

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

Whakawehe 0 ki te -2.

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

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.

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

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

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

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

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

Whakarūnātia.

$$x-1=1 x-1=-1$$

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

$$x=2 x=0$$