Whakaoti mō x (complex solution)
x=4+i
x=4-i
Graph
Tohaina
Kua tāruatia ki te papatopenga
x^{2}-8x+17=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=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 17}}{2}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -8 mō b, me 17 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{-\left(-8\right)±\sqrt{64-4\times 17}}{2}
Pūrua -8.
x=\frac{-\left(-8\right)±\sqrt{64-68}}{2}
Whakareatia -4 ki te 17.
x=\frac{-\left(-8\right)±\sqrt{-4}}{2}
Tāpiri 64 ki te -68.
x=\frac{-\left(-8\right)±2i}{2}
Tuhia te pūtakerua o te -4.
x=\frac{8±2i}{2}
Ko te tauaro o -8 ko 8.
x=\frac{8+2i}{2}
Nā, me whakaoti te whārite x=\frac{8±2i}{2} ina he tāpiri te ±. Tāpiri 8 ki te 2i.
x=4+i
Whakawehe 8+2i ki te 2.
x=\frac{8-2i}{2}
Nā, me whakaoti te whārite x=\frac{8±2i}{2} ina he tango te ±. Tango 2i mai i 8.
x=4-i
Whakawehe 8-2i ki te 2.
x=4+i x=4-i
Kua oti te whārite te whakatau.
x^{2}-8x+17=0
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}-8x+17-17=-17
Me tango 17 mai i ngā taha e rua o te whārite.
x^{2}-8x=-17
Mā te tango i te 17 i a ia ake anō ka toe ko te 0.
x^{2}-8x+\left(-4\right)^{2}=-17+\left(-4\right)^{2}
Whakawehea te -8, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -4. Nā, tāpiria te pūrua o te -4 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.
x^{2}-8x+16=-17+16
Pūrua -4.
x^{2}-8x+16=-1
Tāpiri -17 ki te 16.
\left(x-4\right)^{2}=-1
Tauwehea x^{2}-8x+16. 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-4\right)^{2}}=\sqrt{-1}
Tuhia te pūtakerua o ngā taha e rua o te whārite.
x-4=i x-4=-i
Whakarūnātia.
x=4+i x=4-i
Me tāpiri 4 ki ngā taha e rua o te whārite.
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