x^4+y^4pi+x^2y^2=91 を解きます| Microsoft 数学ソルバー

$${ x }^{ 4 } + { y }^{ 4 } \pi + { x }^{ 2 } { y }^{ 2 } =91$$

x を解く (複素数の解)

$$x=\frac{\sqrt{-2\sqrt{364+y^{4}-4\pi y^{4}}-2y^{2}}}{2}$$

$$x=-\frac{\sqrt{-2\sqrt{364+y^{4}-4\pi y^{4}}-2y^{2}}}{2}$$

$$x=-\frac{\sqrt{2\sqrt{364+y^{4}-4\pi y^{4}}-2y^{2}}}{2}$$

$$x=\frac{\sqrt{2\sqrt{364+y^{4}-4\pi y^{4}}-2y^{2}}}{2}$$

y を解く (複素数の解)

$$y=\frac{i\sqrt{\frac{2\left(\sqrt{364\pi +x^{4}-4\pi x^{4}}+x^{2}\right)}{\pi }}}{2}$$

$$y=-\frac{i\sqrt{\frac{2\left(\sqrt{364\pi +x^{4}-4\pi x^{4}}+x^{2}\right)}{\pi }}}{2}$$

$$y=-\frac{\sqrt{\frac{2\left(\sqrt{364\pi +x^{4}-4\pi x^{4}}-x^{2}\right)}{\pi }}}{2}$$

$$y=\frac{\sqrt{\frac{2\left(\sqrt{364\pi +x^{4}-4\pi x^{4}}-x^{2}\right)}{\pi }}}{2}$$

x を解く

$$x=-\frac{\sqrt{2\left(\sqrt{364+y^{4}-4\pi y^{4}}-y^{2}\right)}}{2}$$

$$x=\frac{\sqrt{2\left(\sqrt{364+y^{4}-4\pi y^{4}}-y^{2}\right)}}{2}\text{, }|y|\leq \frac{\sqrt[4]{91}}{\sqrt[4]{\pi }}$$

y を解く

$$y=-\frac{\sqrt{\frac{2\left(\sqrt{364\pi +x^{4}-4\pi x^{4}}-x^{2}\right)}{\pi }}}{2}$$

$$y=\frac{\sqrt{\frac{2\left(\sqrt{364\pi +x^{4}-4\pi x^{4}}-x^{2}\right)}{\pi }}}{2}\text{, }|x|\leq \sqrt[4]{91}$$