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Whakaoti mō x (complex solution)
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Whakaoti mō x
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Whakaoti mō A (complex solution)
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Whakaoti mō A
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Tohaina

3x\left(A-3i\right)\left(A+3i\right)-AA^{3}=\left(A-3i\right)\left(A+3i\right)\times 9-A^{2}\left(A-3i\right)\left(A+3i\right)
Whakareatia ngā taha e rua o te whārite ki te \left(A-3i\right)\left(A+3i\right).
3x\left(A-3i\right)\left(A+3i\right)-A^{4}=\left(A-3i\right)\left(A+3i\right)\times 9-A^{2}\left(A-3i\right)\left(A+3i\right)
Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 1 me te 3 kia riro ai te 4.
\left(3xA-9ix\right)\left(A+3i\right)-A^{4}=\left(A-3i\right)\left(A+3i\right)\times 9-A^{2}\left(A-3i\right)\left(A+3i\right)
Whakamahia te āhuatanga tohatoha hei whakarea te 3x ki te A-3i.
3xA^{2}+27x-A^{4}=\left(A-3i\right)\left(A+3i\right)\times 9-A^{2}\left(A-3i\right)\left(A+3i\right)
Whakamahia te āhuatanga tuaritanga hei whakarea te 3xA-9ix ki te A+3i ka whakakotahi i ngā kupu rite.
3xA^{2}+27x-A^{4}=\left(A^{2}+9\right)\times 9-A^{2}\left(A-3i\right)\left(A+3i\right)
Whakamahia te āhuatanga tuaritanga hei whakarea te A-3i ki te A+3i ka whakakotahi i ngā kupu rite.
3xA^{2}+27x-A^{4}=9A^{2}+81-A^{2}\left(A-3i\right)\left(A+3i\right)
Whakamahia te āhuatanga tohatoha hei whakarea te A^{2}+9 ki te 9.
3xA^{2}+27x-A^{4}=9A^{2}+81+\left(-A^{3}+3iA^{2}\right)\left(A+3i\right)
Whakamahia te āhuatanga tohatoha hei whakarea te -A^{2} ki te A-3i.
3xA^{2}+27x-A^{4}=9A^{2}+81-A^{4}-9A^{2}
Whakamahia te āhuatanga tuaritanga hei whakarea te -A^{3}+3iA^{2} ki te A+3i ka whakakotahi i ngā kupu rite.
3xA^{2}+27x-A^{4}=81-A^{4}
Pahekotia te 9A^{2} me -9A^{2}, ka 0.
3xA^{2}+27x=81-A^{4}+A^{4}
Me tāpiri te A^{4} ki ngā taha e rua.
3xA^{2}+27x=81
Pahekotia te -A^{4} me A^{4}, ka 0.
\left(3A^{2}+27\right)x=81
Pahekotia ngā kīanga tau katoa e whai ana i te x.
\frac{\left(3A^{2}+27\right)x}{3A^{2}+27}=\frac{81}{3A^{2}+27}
Whakawehea ngā taha e rua ki te 3A^{2}+27.
x=\frac{81}{3A^{2}+27}
Mā te whakawehe ki te 3A^{2}+27 ka wetekia te whakareanga ki te 3A^{2}+27.
x=\frac{27}{A^{2}+9}
Whakawehe 81 ki te 3A^{2}+27.
3x\left(A^{2}+9\right)-AA^{3}=\left(A^{2}+9\right)\times 9-A^{2}\left(A^{2}+9\right)
Whakareatia ngā taha e rua o te whārite ki te A^{2}+9.
3x\left(A^{2}+9\right)-A^{4}=\left(A^{2}+9\right)\times 9-A^{2}\left(A^{2}+9\right)
Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 1 me te 3 kia riro ai te 4.
3xA^{2}+27x-A^{4}=\left(A^{2}+9\right)\times 9-A^{2}\left(A^{2}+9\right)
Whakamahia te āhuatanga tohatoha hei whakarea te 3x ki te A^{2}+9.
3xA^{2}+27x-A^{4}=9A^{2}+81-A^{2}\left(A^{2}+9\right)
Whakamahia te āhuatanga tohatoha hei whakarea te A^{2}+9 ki te 9.
3xA^{2}+27x-A^{4}=9A^{2}+81-A^{4}-9A^{2}
Whakamahia te āhuatanga tohatoha hei whakarea te -A^{2} ki te A^{2}+9.
3xA^{2}+27x-A^{4}=81-A^{4}
Pahekotia te 9A^{2} me -9A^{2}, ka 0.
3xA^{2}+27x=81-A^{4}+A^{4}
Me tāpiri te A^{4} ki ngā taha e rua.
3xA^{2}+27x=81
Pahekotia te -A^{4} me A^{4}, ka 0.
\left(3A^{2}+27\right)x=81
Pahekotia ngā kīanga tau katoa e whai ana i te x.
\frac{\left(3A^{2}+27\right)x}{3A^{2}+27}=\frac{81}{3A^{2}+27}
Whakawehea ngā taha e rua ki te 3A^{2}+27.
x=\frac{81}{3A^{2}+27}
Mā te whakawehe ki te 3A^{2}+27 ka wetekia te whakareanga ki te 3A^{2}+27.
x=\frac{27}{A^{2}+9}
Whakawehe 81 ki te 3A^{2}+27.