Whakaoti i te x^2+3x=-x^4

$$x ^ { 2 } + 3 x = - x ^ { 4 }$$

Whakaoti mō x

$$x=\frac{18^{\frac{2}{3}}\left(\sqrt[3]{\sqrt{741}-27}-\sqrt[3]{\sqrt{741}+27}\right)}{18}\approx -1.213411663$$

$$x=0$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me tāpiri te x^{4} ki ngā taha e rua.

$$x^{2}+3x+x^{4}=0$$

Whakakapia te t mō te x^{2}.

$$t^{2}+t+3=0$$

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 1 mō te b, me te 3 mō te c i te ture pūrua.

$$t=\frac{-1±\sqrt{1^{2}-4\times 1\times 3}}{2}$$

Mahia ngā tātaitai.

$$t=\frac{-1±\sqrt{-11}}{2}$$

Tā te mea e kore te pūrua o tētahi tau tōraro e tautohutia ki te āpure tūturu, kāhore he rongoā.

$$t\in \emptyset$$

I te mea ko t=x^{2}, kāhore ētahi otinga o te whārite taketake.

$$x\in \emptyset$$