Whakaoti i te x^4-20x^2-19=0

$${ x }^{ 4 } -20 { x }^{ 2 } -19=0$$

Whakaoti mō x (complex solution)

$$x=i\sqrt{\sqrt{119}-10}\approx 0.953263927i$$

$$x=-i\sqrt{\sqrt{119}-10}\approx -0-0.953263927i$$

$$x=-\sqrt{\sqrt{119}+10}\approx -4.572604522$$

$$x=\sqrt{\sqrt{119}+10}\approx 4.572604522$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakakapia te t mō te x^{2}.

$$t^{2}-20t-19=0$$

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 -20 mō te b, me te -19 mō te c i te ture pūrua.

$$t=\frac{-\left(-20\right)±\sqrt{\left(-20\right)^{2}-4\times 1\left(-19\right)}}{2}$$

Mahia ngā tātaitai.

$$t=\frac{20±2\sqrt{119}}{2}$$

Whakaotia te whārite t=\frac{20±2\sqrt{119}}{2} ina he tōrunga te ±, ina he tōraro te ±.

$$t=\sqrt{119}+10 t=10-\sqrt{119}$$

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

$$x=-\sqrt{\sqrt{119}+10} x=\sqrt{\sqrt{119}+10} x=-i\sqrt{-\left(10-\sqrt{119}\right)} x=i\sqrt{-\left(10-\sqrt{119}\right)}$$

Whakaoti mō x

$$x=-\sqrt{\sqrt{119}+10}\approx -4.572604522$$

$$x=\sqrt{\sqrt{119}+10}\approx 4.572604522$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakakapia te t mō te x^{2}.

$$t^{2}-20t-19=0$$

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 -20 mō te b, me te -19 mō te c i te ture pūrua.

$$t=\frac{-\left(-20\right)±\sqrt{\left(-20\right)^{2}-4\times 1\left(-19\right)}}{2}$$

Mahia ngā tātaitai.

$$t=\frac{20±2\sqrt{119}}{2}$$

Whakaotia te whārite t=\frac{20±2\sqrt{119}}{2} ina he tōrunga te ±, ina he tōraro te ±.

$$t=\sqrt{119}+10 t=10-\sqrt{119}$$

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

$$x=\sqrt{\sqrt{119}+10} x=-\sqrt{\sqrt{119}+10}$$