Whakaoti mō x (complex solution)
x=1
x=-1
x=-\frac{3\sqrt{10}i}{10}\approx -0-0.948683298i
x=\frac{3\sqrt{10}i}{10}\approx 0.948683298i
Whakaoti mō x
x=-1
x=1
Graph
Tohaina
Kua tāruatia ki te papatopenga
\frac{10}{3}x^{4}-\frac{1}{3}x^{2}-3=0
Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.
\frac{10}{3}t^{2}-\frac{1}{3}t-3=0
Whakakapia te t mō te x^{2}.
t=\frac{-\left(-\frac{1}{3}\right)±\sqrt{\left(-\frac{1}{3}\right)^{2}-4\times \frac{10}{3}\left(-3\right)}}{2\times \frac{10}{3}}
Ka taea ngā whārite katoa o te momo ax^{2}+bx+c=0 te whakaoti mā te ture pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Whakakapia te \frac{10}{3} mō te a, te -\frac{1}{3} mō te b, me te -3 mō te c i te ture pūrua.
t=\frac{\frac{1}{3}±\frac{19}{3}}{\frac{20}{3}}
Mahia ngā tātaitai.
t=1 t=-\frac{9}{10}
Whakaotia te whārite t=\frac{\frac{1}{3}±\frac{19}{3}}{\frac{20}{3}} ina he tōrunga te ±, ina he tōraro te ±.
x=-1 x=1 x=-\frac{3\sqrt{10}i}{10} x=\frac{3\sqrt{10}i}{10}
I te mea ko x=t^{2}, ka riro ngā otinga mā te arotake i te x=±\sqrt{t} mō ia t.
\frac{10}{3}x^{4}-\frac{1}{3}x^{2}-3=0
Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.
\frac{10}{3}t^{2}-\frac{1}{3}t-3=0
Whakakapia te t mō te x^{2}.
t=\frac{-\left(-\frac{1}{3}\right)±\sqrt{\left(-\frac{1}{3}\right)^{2}-4\times \frac{10}{3}\left(-3\right)}}{2\times \frac{10}{3}}
Ka taea ngā whārite katoa o te momo ax^{2}+bx+c=0 te whakaoti mā te ture pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Whakakapia te \frac{10}{3} mō te a, te -\frac{1}{3} mō te b, me te -3 mō te c i te ture pūrua.
t=\frac{\frac{1}{3}±\frac{19}{3}}{\frac{20}{3}}
Mahia ngā tātaitai.
t=1 t=-\frac{9}{10}
Whakaotia te whārite t=\frac{\frac{1}{3}±\frac{19}{3}}{\frac{20}{3}} ina he tōrunga te ±, ina he tōraro te ±.
x=1 x=-1
I te mea ko x=t^{2}, ka riro ngā otinga mā te arotake i te x=±\sqrt{t} mō t tōrunga.
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