Whakaoti i te 1/x=-x+2.5

$$\frac{ 1 }{ x } = -x+2.5$$

Whakaoti mō x

$$x=0.5$$

$$x=2$$

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.

$$1=-xx+x\times 2.5$$

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

$$1=-x^{2}+x\times 2.5$$

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

$$-x^{2}+x\times 2.5=1$$

Tangohia te 1 mai i ngā taha e rua.

$$-x^{2}+x\times 2.5-1=0$$

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.

$$-x^{2}+2.5x-1=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 2.5 mō b, me -1 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-2.5±\sqrt{2.5^{2}-4\left(-1\right)\left(-1\right)}}{2\left(-1\right)}$$

Pūruatia 2.5 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x=\frac{-2.5±\sqrt{6.25-4\left(-1\right)\left(-1\right)}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-2.5±\sqrt{6.25+4\left(-1\right)}}{2\left(-1\right)}$$

Whakareatia 4 ki te -1.

$$x=\frac{-2.5±\sqrt{6.25-4}}{2\left(-1\right)}$$

Tāpiri 6.25 ki te -4.

$$x=\frac{-2.5±\sqrt{2.25}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 2.25.

$$x=\frac{-2.5±\frac{3}{2}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-2.5±\frac{3}{2}}{-2}$$

Nā, me whakaoti te whārite x=\frac{-2.5±\frac{3}{2}}{-2} ina he tāpiri te ±. Tāpiri -2.5 ki te \frac{3}{2} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

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

Whakawehe -1 ki te -2.

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

Nā, me whakaoti te whārite x=\frac{-2.5±\frac{3}{2}}{-2} ina he tango te ±. Tango \frac{3}{2} mai i -2.5 mā te kimi i te tauraro pātahi me te tango i ngā taurunga, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

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

Whakawehe -4 ki te -2.

$$x=2$$

Kua oti te whārite te whakatau.

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

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.

$$1=-xx+x\times 2.5$$

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

$$1=-x^{2}+x\times 2.5$$

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

$$-x^{2}+x\times 2.5=1$$

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.

$$-x^{2}+2.5x=1$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-x^{2}+2.5x}{-1}=\frac{1}{-1}$$

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

$$x^{2}+\frac{2.5}{-1}x=\frac{1}{-1}$$

Whakawehe 2.5 ki te -1.

$$x^{2}-2.5x=\frac{1}{-1}$$

Whakawehe 1 ki te -1.

$$x^{2}-2.5x=-1$$

Whakawehea te -2.5, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -1.25. Nā, tāpiria te pūrua o te -1.25 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-2.5x+\left(-1.25\right)^{2}=-1+\left(-1.25\right)^{2}$$

Pūruatia -1.25 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-2.5x+1.5625=-1+1.5625$$

Tāpiri -1 ki te 1.5625.

$$x^{2}-2.5x+1.5625=0.5625$$

Tauwehea te x^{2}-2.5x+1.5625. Ko te tikanga, ina ko x^{2}+bx+c he pūrua tika, ka taea te tauwehe i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-1.25\right)^{2}=0.5625$$

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

$$\sqrt{\left(x-1.25\right)^{2}}=\sqrt{0.5625}$$

Whakarūnātia.

$$x-1.25=\frac{3}{4} x-1.25=-\frac{3}{4}$$

Me tāpiri 1.25 ki ngā taha e rua o te whārite.

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