Whakaoti i te a^4-64a^2+25*36=0

$$a ^ { 4 } - 64 a ^ { 2 } + 25 \times 36 = 0$$

Whakaoti mō a (complex solution)

$$a=\sqrt{31}-1\approx 4.567764363$$

$$a=1-\sqrt{31}\approx -4.567764363$$

$$a=-\left(\sqrt{31}+1\right)\approx -6.567764363$$

$$a=\sqrt{31}+1\approx 6.567764363$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te 25 ki te 36, ka 900.

$$a^{4}-64a^{2}+900=0$$

Whakakapia te t mō te a^{2}.

$$t^{2}-64t+900=0$$

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 -64 mō te b, me te 900 mō te c i te ture pūrua.

$$t=\frac{-\left(-64\right)±\sqrt{\left(-64\right)^{2}-4\times 1\times 900}}{2}$$

Mahia ngā tātaitai.

$$t=\frac{64±4\sqrt{31}}{2}$$

Whakaotia te whārite t=\frac{64±4\sqrt{31}}{2} ina he tōrunga te ±, ina he tōraro te ±.

$$t=2\sqrt{31}+32 t=32-2\sqrt{31}$$

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

$$a=-\left(\sqrt{31}+1\right) a=\sqrt{31}+1 a=1-\sqrt{31} a=-\left(1-\sqrt{31}\right)$$

Whakaoti mō a

$$a=1-\sqrt{31}\approx -4.567764363$$

$$a=\sqrt{31}-1\approx 4.567764363$$

$$a=\sqrt{31}+1\approx 6.567764363$$

$$a=-\sqrt{31}-1\approx -6.567764363$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te 25 ki te 36, ka 900.

$$a^{4}-64a^{2}+900=0$$

Whakakapia te t mō te a^{2}.

$$t^{2}-64t+900=0$$

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 -64 mō te b, me te 900 mō te c i te ture pūrua.

$$t=\frac{-\left(-64\right)±\sqrt{\left(-64\right)^{2}-4\times 1\times 900}}{2}$$

Mahia ngā tātaitai.

$$t=\frac{64±4\sqrt{31}}{2}$$

Whakaotia te whārite t=\frac{64±4\sqrt{31}}{2} ina he tōrunga te ±, ina he tōraro te ±.

$$t=2\sqrt{31}+32 t=32-2\sqrt{31}$$

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

$$a=\sqrt{31}+1 a=-\left(\sqrt{31}+1\right) a=-\left(1-\sqrt{31}\right) a=1-\sqrt{31}$$