Whakaoti i te x+33/12-x=x

$$\frac { x + 33 } { 12 - x } = x$$

Whakaoti mō x (complex solution)

$$x=\frac{11+\sqrt{11}i}{2}\approx 5.5+1.658312395i$$

$$x=\frac{-\sqrt{11}i+11}{2}\approx 5.5-1.658312395i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki 12 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te -x+12.

$$x+33=x\left(-x+12\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te -x+12.

$$x+33=-x^{2}+12x$$

Me tāpiri te x^{2} ki ngā taha e rua.

$$x+33+x^{2}=12x$$

Tangohia te 12x mai i ngā taha e rua.

$$x+33+x^{2}-12x=0$$

Pahekotia te x me -12x, ka -11x.

$$-11x+33+x^{2}=0$$

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.

$$x^{2}-11x+33=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -11 mō b, me 33 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-11\right)±\sqrt{\left(-11\right)^{2}-4\times 33}}{2}$$

Pūrua -11.

$$x=\frac{-\left(-11\right)±\sqrt{121-4\times 33}}{2}$$

Whakareatia -4 ki te 33.

$$x=\frac{-\left(-11\right)±\sqrt{121-132}}{2}$$

Tāpiri 121 ki te -132.

$$x=\frac{-\left(-11\right)±\sqrt{-11}}{2}$$

Tuhia te pūtakerua o te -11.

$$x=\frac{-\left(-11\right)±\sqrt{11}i}{2}$$

Ko te tauaro o -11 ko 11.

$$x=\frac{11±\sqrt{11}i}{2}$$

Nā, me whakaoti te whārite x=\frac{11±\sqrt{11}i}{2} ina he tāpiri te ±. Tāpiri 11 ki te i\sqrt{11}.

$$x=\frac{11+\sqrt{11}i}{2}$$

Nā, me whakaoti te whārite x=\frac{11±\sqrt{11}i}{2} ina he tango te ±. Tango i\sqrt{11} mai i 11.

$$x=\frac{-\sqrt{11}i+11}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{11+\sqrt{11}i}{2} x=\frac{-\sqrt{11}i+11}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki 12 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te -x+12.

$$x+33=x\left(-x+12\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te -x+12.

$$x+33=-x^{2}+12x$$

Me tāpiri te x^{2} ki ngā taha e rua.

$$x+33+x^{2}=12x$$

Tangohia te 12x mai i ngā taha e rua.

$$x+33+x^{2}-12x=0$$

Pahekotia te x me -12x, ka -11x.

$$-11x+33+x^{2}=0$$

Tangohia te 33 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-11x+x^{2}=-33$$

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.

$$x^{2}-11x=-33$$

Whakawehea te -11, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{11}{2}. Nā, tāpiria te pūrua o te -\frac{11}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-11x+\left(-\frac{11}{2}\right)^{2}=-33+\left(-\frac{11}{2}\right)^{2}$$

Pūruatia -\frac{11}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-11x+\frac{121}{4}=-33+\frac{121}{4}$$

Tāpiri -33 ki te \frac{121}{4}.

$$x^{2}-11x+\frac{121}{4}=-\frac{11}{4}$$

Tauwehea x^{2}-11x+\frac{121}{4}. 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}.

$$\left(x-\frac{11}{2}\right)^{2}=-\frac{11}{4}$$

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

$$\sqrt{\left(x-\frac{11}{2}\right)^{2}}=\sqrt{-\frac{11}{4}}$$

Whakarūnātia.

$$x-\frac{11}{2}=\frac{\sqrt{11}i}{2} x-\frac{11}{2}=-\frac{\sqrt{11}i}{2}$$

Me tāpiri \frac{11}{2} ki ngā taha e rua o te whārite.

$$x=\frac{11+\sqrt{11}i}{2} x=\frac{-\sqrt{11}i+11}{2}$$