Whakaoti mō x (complex solution)
x=-\sqrt{2}i\approx -0-1.414213562i
x=\sqrt{2}i\approx 1.414213562i
Graph
Tohaina
Kua tāruatia ki te papatopenga
x^{2}+2=0
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^{2}.
x^{2}=-2
Tangohia te 2 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.
x=\sqrt{2}i x=-\sqrt{2}i
Kua oti te whārite te whakatau.
x^{2}+2=0
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^{2}.
x=\frac{0±\sqrt{0^{2}-4\times 2}}{2}
Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me 2 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\times 2}}{2}
Pūrua 0.
x=\frac{0±\sqrt{-8}}{2}
Whakareatia -4 ki te 2.
x=\frac{0±2\sqrt{2}i}{2}
Tuhia te pūtakerua o te -8.
x=\sqrt{2}i
Nā, me whakaoti te whārite x=\frac{0±2\sqrt{2}i}{2} ina he tāpiri te ±.
x=-\sqrt{2}i
Nā, me whakaoti te whārite x=\frac{0±2\sqrt{2}i}{2} ina he tango te ±.
x=\sqrt{2}i x=-\sqrt{2}i
Kua oti te whārite te whakatau.
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