Whakaoti i te 3x^4+84=52x^2

$$3 x ^ { 4 } + 84 = 52 x ^ { 2 }$$

Whakaoti mō x

$$x = -\frac{\sqrt{78 - 6 \sqrt{106}}}{3} \approx -1.342726048$$

$$x = \frac{\sqrt{78 - 6 \sqrt{106}}}{3} \approx 1.342726048$$

$$x = \frac{\sqrt{6 \sqrt{106} + 78}}{3} \approx 3.940865399$$

$$x = -\frac{\sqrt{6 \sqrt{106} + 78}}{3} \approx -3.940865399$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 52x^{2} mai i ngā taha e rua.

$$3x^{4}+84-52x^{2}=0$$

Whakakapia te t mō te x^{2}.

$$3t^{2}-52t+84=0$$

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 3 mō te a, te -52 mō te b, me te 84 mō te c i te ture pūrua.

$$t=\frac{-\left(-52\right)±\sqrt{\left(-52\right)^{2}-4\times 3\times 84}}{2\times 3}$$

Mahia ngā tātaitai.

$$t=\frac{52±4\sqrt{106}}{6}$$

Whakaotia te whārite t=\frac{52±4\sqrt{106}}{6} ina he tōrunga te ±, ina he tōraro te ±.

$$t=\frac{2\sqrt{106}+26}{3} t=\frac{26-2\sqrt{106}}{3}$$

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

$$x=\frac{\sqrt{\frac{8\sqrt{106}+104}{3}}}{2} x=-\frac{\sqrt{\frac{8\sqrt{106}+104}{3}}}{2} x=\frac{\sqrt{\frac{104-8\sqrt{106}}{3}}}{2} x=-\frac{\sqrt{\frac{104-8\sqrt{106}}{3}}}{2}$$