Whakaoti i te x^4-x^2+72=0

$$x ^ { 4 } - x ^ { 2 } + 72 = 0$$

Whakaoti mō x (complex solution)

$$x=\sqrt[4]{72}e^{\frac{-\arctan(\sqrt{287})i+2\pi i}{2}}\approx -2.119585027+1.998159325i$$

$$x=\sqrt[4]{72}e^{-\frac{\arctan(\sqrt{287})i}{2}}\approx 2.119585027-1.998159325i$$

$$x=\sqrt[4]{72}e^{\frac{\arctan(\sqrt{287})i+2\pi i}{2}}\approx -2.119585027-1.998159325i$$

$$x=\sqrt[4]{72}e^{\frac{\arctan(\sqrt{287})i}{2}}\approx 2.119585027+1.998159325i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakakapia te t mō te x^{2}.

$$t^{2}-t+72=0$$

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 1 mō te a, te -1 mō te b, me te 72 mō te c i te ture pūrua.

$$t=\frac{-\left(-1\right)±\sqrt{\left(-1\right)^{2}-4\times 1\times 72}}{2}$$

Mahia ngā tātaitai.

$$t=\frac{1±\sqrt{-287}}{2}$$

Whakaotia te whārite t=\frac{1±\sqrt{-287}}{2} ina he tōrunga te ±, ina he tōraro te ±.

$$t=\frac{1+\sqrt{287}i}{2} t=\frac{-\sqrt{287}i+1}{2}$$

I te mea ko x=t^{2}, ka riro ngā otinga mā te arotake i te x=±\sqrt{t} mō ia t.

$$x=\sqrt[4]{72}e^{\frac{\arctan(\sqrt{287})i+2\pi i}{2}} x=\sqrt[4]{72}e^{\frac{\arctan(\sqrt{287})i}{2}} x=\sqrt[4]{72}e^{-\frac{\arctan(\sqrt{287})i}{2}} x=\sqrt[4]{72}e^{\frac{-\arctan(\sqrt{287})i+2\pi i}{2}}$$