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

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

Whakaoti mō x

$$x=2$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Tangohia te 1 mai i ngā taha e rua.

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

Tangohia te 1 i te 1, ka 0.

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

Tauwehea te x.

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

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

$$x=0 x=2$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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.

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

Me tango 1 mai i ngā taha e rua o te whārite.

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

Mā te tango i te 1 i a ia ake anō ka toe ko te 0.

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

Tango 1 mai i 1.

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

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

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

Tuhia te pūtakerua o te \left(-2\right)^{2}.

$$x=\frac{-\left(-2\right)±2}{2}$$

Ko te tauaro o -2 ko 2.

$$x=\frac{2±2}{2}$$

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

$$x=\frac{4}{2}$$

Whakawehe 4 ki te 2.

$$x=2$$

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

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

Whakawehe 0 ki te 2.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=2 x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 1 mai i ngā taha e rua.

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

Tangohia te 1 i te 1, ka 0.

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

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.

$$x=2 x=0$$