Whakaoti i te x^4+34x^2+225=0

$$x ^ { 4 } + 34 x ^ { 2 } + 225 = 0$$

Whakaoti mō x (complex solution)

$$x=3i$$

$$x=-3i$$

$$x=-5i$$

$$x=5i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakakapia te t mō te x^{2}.

$$t^{2}+34t+225=0$$

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 34 mō te b, me te 225 mō te c i te ture pūrua.

$$t=\frac{-34±\sqrt{34^{2}-4\times 1\times 225}}{2}$$

Mahia ngā tātaitai.

$$t=\frac{-34±16}{2}$$

Whakaotia te whārite t=\frac{-34±16}{2} ina he tōrunga te ±, ina he tōraro te ±.

$$t=-9 t=-25$$

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

$$x=-3i x=3i x=-5i x=5i$$