Whakaoti i te x^4+4/x^4=4

$$x ^ { 4 } + \frac { 4 } { x ^ { 4 } } = 4$$

Whakaoti mō x (complex solution)

$$x=\sqrt[4]{2}i\approx 1.189207115i$$

$$x=\sqrt[4]{2}\approx 1.189207115$$

$$x=-\sqrt[4]{2}\approx -1.189207115$$

$$x=-\sqrt[4]{2}i\approx -0-1.189207115i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x^{4}.

$$x^{4}x^{4}+4=4x^{4}$$

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 4 me te 4 kia riro ai te 8.

$$x^{8}+4=4x^{4}$$

Tangohia te 4x^{4} mai i ngā taha e rua.

$$x^{8}+4-4x^{4}=0$$

Whakakapia te t mō te x^{4}.

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

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

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

Mahia ngā tātaitai.

$$t=\frac{4±0}{2}$$

He ōrite ngā whakatau.

$$t=2$$

Mai i te x=t^{4}, ka taea ngā otinga mā te whakaoti te whārite mō ia t.

$$x=\sqrt[4]{2} x=\sqrt[4]{2}i x=-\sqrt[4]{2} x=-\sqrt[4]{2}i$$

Whakaoti mō x

$$x=\sqrt[4]{2}\approx 1.189207115$$

$$x=-\sqrt[4]{2}\approx -1.189207115$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x^{4}.

$$x^{4}x^{4}+4=4x^{4}$$

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 4 me te 4 kia riro ai te 8.

$$x^{8}+4=4x^{4}$$

Tangohia te 4x^{4} mai i ngā taha e rua.

$$x^{8}+4-4x^{4}=0$$

Whakakapia te t mō te x^{4}.

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

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

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

Mahia ngā tātaitai.

$$t=\frac{4±0}{2}$$

He ōrite ngā whakatau.

$$t=2$$

I te mea ko x=t^{4}, ka riro ngā otinga mā te arotake i te x=±\sqrt[4]{t} mō t tōrunga.

$$x=-\sqrt[4]{2} x=\sqrt[4]{2}$$