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Whakaoti mō x_0
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x_{0}^{2}-2x_{0}=-3
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_{0}^{2}-2x_{0}-\left(-3\right)=-3-\left(-3\right)
Me tāpiri 3 ki ngā taha e rua o te whārite.
x_{0}^{2}-2x_{0}-\left(-3\right)=0
Mā te tango i te -3 i a ia ake anō ka toe ko te 0.
x_{0}^{2}-2x_{0}+3=0
Tango -3 mai i 0.
x_{0}=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\times 3}}{2}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -2 mō b, me 3 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x_{0}=\frac{-\left(-2\right)±\sqrt{4-4\times 3}}{2}
Pūrua -2.
x_{0}=\frac{-\left(-2\right)±\sqrt{4-12}}{2}
Whakareatia -4 ki te 3.
x_{0}=\frac{-\left(-2\right)±\sqrt{-8}}{2}
Tāpiri 4 ki te -12.
x_{0}=\frac{-\left(-2\right)±2\sqrt{2}i}{2}
Tuhia te pūtakerua o te -8.
x_{0}=\frac{2±2\sqrt{2}i}{2}
Ko te tauaro o -2 ko 2.
x_{0}=\frac{2+2\sqrt{2}i}{2}
Nā, me whakaoti te whārite x_{0}=\frac{2±2\sqrt{2}i}{2} ina he tāpiri te ±. Tāpiri 2 ki te 2i\sqrt{2}.
x_{0}=1+\sqrt{2}i
Whakawehe 2+2i\sqrt{2} ki te 2.
x_{0}=\frac{-2\sqrt{2}i+2}{2}
Nā, me whakaoti te whārite x_{0}=\frac{2±2\sqrt{2}i}{2} ina he tango te ±. Tango 2i\sqrt{2} mai i 2.
x_{0}=-\sqrt{2}i+1
Whakawehe 2-2i\sqrt{2} ki te 2.
x_{0}=1+\sqrt{2}i x_{0}=-\sqrt{2}i+1
Kua oti te whārite te whakatau.
x_{0}^{2}-2x_{0}=-3
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_{0}^{2}-2x_{0}+1=-3+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_{0}^{2}-2x_{0}+1=-2
Tāpiri -3 ki te 1.
\left(x_{0}-1\right)^{2}=-2
Tauwehea x_{0}^{2}-2x_{0}+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}.
\sqrt{\left(x_{0}-1\right)^{2}}=\sqrt{-2}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x_{0}-1=\sqrt{2}i x_{0}-1=-\sqrt{2}i
Whakarūnātia.
x_{0}=1+\sqrt{2}i x_{0}=-\sqrt{2}i+1
Me tāpiri 1 ki ngā taha e rua o te whārite.