Whakaoti i te x^4-6x^2-27=0

$$x ^ { 4 } - 6 x ^ { 2 } - 27 = 0$$

Whakaoti mō x (complex solution)

$$x=3$$

$$x=-3$$

$$x=-\sqrt{3}i\approx -0-1.732050808i$$

$$x=\sqrt{3}i\approx 1.732050808i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakakapia te t mō te x^{2}.

$$t^{2}-6t-27=0$$

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 -6 mō te b, me te -27 mō te c i te ture pūrua.

$$t=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\times 1\left(-27\right)}}{2}$$

Mahia ngā tātaitai.

$$t=\frac{6±12}{2}$$

Whakaotia te whārite t=\frac{6±12}{2} ina he tōrunga te ±, ina he tōraro te ±.

$$t=9 t=-3$$

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

$$x=-3 x=3 x=-\sqrt{3}i x=\sqrt{3}i$$

Whakaoti mō x

$$x=-3$$

$$x=3$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakakapia te t mō te x^{2}.

$$t^{2}-6t-27=0$$

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 -6 mō te b, me te -27 mō te c i te ture pūrua.

$$t=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\times 1\left(-27\right)}}{2}$$

Mahia ngā tātaitai.

$$t=\frac{6±12}{2}$$

Whakaotia te whārite t=\frac{6±12}{2} ina he tōrunga te ±, ina he tōraro te ±.

$$t=9 t=-3$$

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

$$x=3 x=-3$$