Whakaoti i te x^2+1/x^2=27

$$x ^ { 2 } + \frac { 1 } { x ^ { 2 } } = 27$$

Whakaoti mō x

$$x=\frac{-\sqrt{29}-5}{2}\approx -5.192582404$$

$$x = \frac{\sqrt{29} + 5}{2} \approx 5.192582404$$

$$x=\frac{\sqrt{29}-5}{2}\approx 0.192582404$$

$$x=\frac{5-\sqrt{29}}{2}\approx -0.192582404$$

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^{2}.

$$x^{2}x^{2}+1=27x^{2}$$

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 2 me te 2 kia riro ai te 4.

$$x^{4}+1=27x^{2}$$

Tangohia te 27x^{2} mai i ngā taha e rua.

$$x^{4}+1-27x^{2}=0$$

Whakakapia te t mō te x^{2}.

$$t^{2}-27t+1=0$$

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 -27 mō te b, me te 1 mō te c i te ture pūrua.

$$t=\frac{-\left(-27\right)±\sqrt{\left(-27\right)^{2}-4\times 1\times 1}}{2}$$

Mahia ngā tātaitai.

$$t=\frac{27±5\sqrt{29}}{2}$$

Whakaotia te whārite t=\frac{27±5\sqrt{29}}{2} ina he tōrunga te ±, ina he tōraro te ±.

$$t=\frac{5\sqrt{29}+27}{2} t=\frac{27-5\sqrt{29}}{2}$$

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

$$x=\frac{\sqrt{29}+5}{2} x=-\frac{\sqrt{29}+5}{2} x=-\frac{5-\sqrt{29}}{2} x=\frac{5-\sqrt{29}}{2}$$