Whakaoti i te 1-1x^4-5x^2+4=0

$$1 - 1 x ^ { 4 } - 5 x ^ { 2 } + 4 = 0$$

Whakaoti mō x (complex solution)

$$x=\frac{5^{\frac{3}{4}}i+\sqrt[4]{5}i}{2}\approx 2.419525153i$$

$$x=\frac{-5^{\frac{3}{4}}i-\sqrt[4]{5}i}{2}\approx -2.419525153i$$

$$x=-\frac{\sqrt{6\sqrt{5}-10}}{2}\approx -0.924176372$$

$$x=\frac{\sqrt{6\sqrt{5}-10}}{2}\approx 0.924176372$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tāpirihia te 1 ki te 4, ka 5.

$$5-x^{4}-5x^{2}=0$$

Whakakapia te t mō te x^{2}.

$$-t^{2}-5t+5=0$$

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 -5 mō te b, me te 5 mō te c i te ture pūrua.

$$t=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\left(-1\right)\times 5}}{-2}$$

Mahia ngā tātaitai.

$$t=\frac{5±3\sqrt{5}}{-2}$$

Whakaotia te whārite t=\frac{5±3\sqrt{5}}{-2} ina he tōrunga te ±, ina he tōraro te ±.

$$t=\frac{-3\sqrt{5}-5}{2} t=\frac{3\sqrt{5}-5}{2}$$

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

$$x=-i\sqrt{\frac{3\sqrt{5}+5}{2}} x=i\sqrt{\frac{3\sqrt{5}+5}{2}} x=-\sqrt{\frac{3\sqrt{5}-5}{2}} x=\sqrt{\frac{3\sqrt{5}-5}{2}}$$

Whakaoti mō x

$$x=-\frac{\sqrt{6\sqrt{5}-10}}{2}\approx -0.924176372$$

$$x=\frac{\sqrt{6\sqrt{5}-10}}{2}\approx 0.924176372$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tāpirihia te 1 ki te 4, ka 5.

$$5-x^{4}-5x^{2}=0$$

Whakakapia te t mō te x^{2}.

$$-t^{2}-5t+5=0$$

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 -5 mō te b, me te 5 mō te c i te ture pūrua.

$$t=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\left(-1\right)\times 5}}{-2}$$

Mahia ngā tātaitai.

$$t=\frac{5±3\sqrt{5}}{-2}$$

Whakaotia te whārite t=\frac{5±3\sqrt{5}}{-2} ina he tōrunga te ±, ina he tōraro te ±.

$$t=\frac{-3\sqrt{5}-5}{2} t=\frac{3\sqrt{5}-5}{2}$$

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

$$x=\frac{\sqrt{6\sqrt{5}-10}}{2} x=-\frac{\sqrt{6\sqrt{5}-10}}{2}$$