Whakaoti i te 9x^4+5x^2-4=0

$$9 x ^ { 4 } + 5 x ^ { 2 } - 4 = 0$$

Whakaoti mō x (complex solution)

$$x=\frac{2}{3}\approx 0.666666667$$

$$x=-\frac{2}{3}\approx -0.666666667$$

$$x=-i$$

$$x=i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakakapia te t mō te x^{2}.

$$9t^{2}+5t-4=0$$

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 9 mō te a, te 5 mō te b, me te -4 mō te c i te ture pūrua.

$$t=\frac{-5±\sqrt{5^{2}-4\times 9\left(-4\right)}}{2\times 9}$$

Mahia ngā tātaitai.

$$t=\frac{-5±13}{18}$$

Whakaotia te whārite t=\frac{-5±13}{18} ina he tōrunga te ±, ina he tōraro te ±.

$$t=\frac{4}{9} t=-1$$

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

$$x=-\frac{2}{3} x=\frac{2}{3} x=-i x=i$$

Whakaoti mō x

$$x=-\frac{2}{3}\approx -0.666666667$$

$$x=\frac{2}{3}\approx 0.666666667$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakakapia te t mō te x^{2}.

$$9t^{2}+5t-4=0$$

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 9 mō te a, te 5 mō te b, me te -4 mō te c i te ture pūrua.

$$t=\frac{-5±\sqrt{5^{2}-4\times 9\left(-4\right)}}{2\times 9}$$

Mahia ngā tātaitai.

$$t=\frac{-5±13}{18}$$

Whakaotia te whārite t=\frac{-5±13}{18} ina he tōrunga te ±, ina he tōraro te ±.

$$t=\frac{4}{9} t=-1$$

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

$$x=\frac{2}{3} x=-\frac{2}{3}$$