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

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

Whakaoti mō x

$$x=\sqrt{2}+1\approx 2.414213562$$

$$x=1-\sqrt{2}\approx -0.414213562$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x.

$$-xx+x\times 2=-1$$

Whakareatia te x ki te x, ka x^{2}.

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

Me tāpiri te 1 ki ngā taha e rua.

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

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.

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

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

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

Pūrua 2.

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

Whakareatia -4 ki te -1.

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

Tāpiri 4 ki te 4.

$$x=\frac{-2±\sqrt{8}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 8.

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

Whakareatia 2 ki te -1.

$$x=\frac{-2±2\sqrt{2}}{-2}$$

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

$$x=\frac{2\sqrt{2}-2}{-2}$$

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

$$x=1-\sqrt{2}$$

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

$$x=\frac{-2\sqrt{2}-2}{-2}$$

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

$$x=\sqrt{2}+1$$

Kua oti te whārite te whakatau.

$$x=1-\sqrt{2} x=\sqrt{2}+1$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x.

$$-xx+x\times 2=-1$$

Whakareatia te x ki te x, ka x^{2}.

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

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

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

Whakawehea ngā taha e rua ki te -1.

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

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

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

Whakawehe 2 ki te -1.

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

Whakawehe -1 ki te -1.

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

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.

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

Tāpiri 1 ki te 1.

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

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}.

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

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

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

Whakarūnātia.

$$x-1=\sqrt{2} x-1=-\sqrt{2}$$

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

$$x=\sqrt{2}+1 x=1-\sqrt{2}$$