Whakaoti i te x^4-8x^2-4=0

$${ x }^{ 4 } -8 { x }^{ 2 } -4=0$$

Whakaoti mō x (complex solution)

$$x=i\sqrt{2\left(\sqrt{5}-2\right)}\approx 0.687121499i$$

$$x=-i\sqrt{2\left(\sqrt{5}-2\right)}\approx -0-0.687121499i$$

$$x=-\sqrt{2\left(\sqrt{5}+2\right)}\approx -2.91069338$$

$$x=\sqrt{2\left(\sqrt{5}+2\right)}\approx 2.91069338$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakakapia te t mō te x^{2}.

$$t^{2}-8t-4=0$$

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 -8 mō te b, me te -4 mō te c i te ture pūrua.

$$t=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 1\left(-4\right)}}{2}$$

Mahia ngā tātaitai.

$$t=\frac{8±4\sqrt{5}}{2}$$

Whakaotia te whārite t=\frac{8±4\sqrt{5}}{2} ina he tōrunga te ±, ina he tōraro te ±.

$$t=2\sqrt{5}+4 t=4-2\sqrt{5}$$

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

$$x=-\sqrt{2\sqrt{5}+4} x=\sqrt{2\sqrt{5}+4} x=-i\sqrt{-\left(4-2\sqrt{5}\right)} x=i\sqrt{-\left(4-2\sqrt{5}\right)}$$

Whakaoti mō x

$$x=-\sqrt{2\left(\sqrt{5}+2\right)}\approx -2.91069338$$

$$x=\sqrt{2\left(\sqrt{5}+2\right)}\approx 2.91069338$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakakapia te t mō te x^{2}.

$$t^{2}-8t-4=0$$

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 -8 mō te b, me te -4 mō te c i te ture pūrua.

$$t=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 1\left(-4\right)}}{2}$$

Mahia ngā tātaitai.

$$t=\frac{8±4\sqrt{5}}{2}$$

Whakaotia te whārite t=\frac{8±4\sqrt{5}}{2} ina he tōrunga te ±, ina he tōraro te ±.

$$t=2\sqrt{5}+4 t=4-2\sqrt{5}$$

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

$$x=\frac{\sqrt{8\sqrt{5}+16}}{2} x=-\frac{\sqrt{8\sqrt{5}+16}}{2}$$