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

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

Whakaoti mō x (complex solution)

$$x=\sqrt{5}\approx 2.236067977$$

$$x=-\sqrt{5}\approx -2.236067977$$

$$x=-2i$$

$$x=2i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakakapia te t mō te x^{2}.

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

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 -20 mō te c i te ture pūrua.

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

Mahia ngā tātaitai.

$$t=\frac{1±9}{2}$$

Whakaotia te whārite t=\frac{1±9}{2} ina he tōrunga te ±, ina he tōraro te ±.

$$t=5 t=-4$$

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

$$x=-\sqrt{5} x=\sqrt{5} x=-2i x=2i$$

Whakaoti mō x

$$x=-\sqrt{5}\approx -2.236067977$$

$$x=\sqrt{5}\approx 2.236067977$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakakapia te t mō te x^{2}.

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

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 -20 mō te c i te ture pūrua.

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

Mahia ngā tātaitai.

$$t=\frac{1±9}{2}$$

Whakaotia te whārite t=\frac{1±9}{2} ina he tōrunga te ±, ina he tōraro te ±.

$$t=5 t=-4$$

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

$$x=\sqrt{5} x=-\sqrt{5}$$