Whakaoti i te (x^2-9)^2=0

$$( x ^ { 2 } - 9 ) ^ { 2 } = 0$$

Whakaoti mō x

$$x=3$$

$$x=-3$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x^{2}-9\right)^{2}.

$$\left(x^{2}\right)^{2}-18x^{2}+81=0$$

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te 2 me te 2 kia riro ai te 4.

$$x^{4}-18x^{2}+81=0$$

Whakakapia te t mō te x^{2}.

$$t^{2}-18t+81=0$$

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 -18 mō te b, me te 81 mō te c i te ture pūrua.

$$t=\frac{-\left(-18\right)±\sqrt{\left(-18\right)^{2}-4\times 1\times 81}}{2}$$

Mahia ngā tātaitai.

$$t=\frac{18±0}{2}$$

He ōrite ngā whakatau.

$$t=9$$

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

$$x=-3 x=3$$