Whakaoti i te 24*x^2+1/x^2=27

$$24 \cdot x ^ { 2 } + \frac { 1 } { x ^ { 2 } } = 27$$

Whakaoti mō x

$$x = -\frac{\sqrt{3 \sqrt{633} + 81}}{12} \approx -1.042427968$$

$$x = \frac{\sqrt{3 \sqrt{633} + 81}}{12} \approx 1.042427968$$

$$x=\frac{\sqrt{81-3\sqrt{633}}}{12}\approx 0.195816067$$

$$x=-\frac{\sqrt{81-3\sqrt{633}}}{12}\approx -0.195816067$$

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}.

$$24x^{2}x^{2}+1=27x^{2}$$

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.

$$24x^{4}+1=27x^{2}$$

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

$$24x^{4}+1-27x^{2}=0$$

Whakakapia te t mō te x^{2}.

$$24t^{2}-27t+1=0$$

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

$$t=\frac{-\left(-27\right)±\sqrt{\left(-27\right)^{2}-4\times 24\times 1}}{2\times 24}$$

Mahia ngā tātaitai.

$$t=\frac{27±\sqrt{633}}{48}$$

Whakaotia te whārite t=\frac{27±\sqrt{633}}{48} ina he tōrunga te ±, ina he tōraro te ±.

$$t=\frac{\sqrt{633}}{48}+\frac{9}{16} t=-\frac{\sqrt{633}}{48}+\frac{9}{16}$$

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

$$x=\frac{\sqrt{\frac{\sqrt{633}}{3}+9}}{4} x=-\frac{\sqrt{\frac{\sqrt{633}}{3}+9}}{4} x=\frac{\sqrt{-\frac{\sqrt{633}}{3}+9}}{4} x=-\frac{\sqrt{-\frac{\sqrt{633}}{3}+9}}{4}$$