\u8fd9\u6bb5\u65f6\u95f4\u5076\u7136\u5237\u5230\u4e00\u9053\u6211\u8fd8\u662f\u9ad8\u4e2d\u751f\u7684\u65f6\u5019\u5c31\u89c1\u8fc7\u7684\u770b\u8d77\u6765\u7b80\u5355\u4f46\u662f\u5b9e\u9645\u4e0a\u5e76\u4e0d\u7b97\u5f88\u7b80\u5355\u7684\u6570\u5b66\u9898\uff0c\u60f3\u7740\u73b0\u5728\u7684\u77e5\u8bc6\u50a8\u5907\u5e94\u8be5\u8db3\u591f\u89e3\u51b3\u8fd9\u9053\u9898\u4e86\uff0c\u6240\u4ee5\u8bb0\u5f55\u4e00\u4e0b.<\/p>\n\n\n\n
\u5df2\u77e5\\(x,y,z\\)\u4e3a\u4e09\u6b63\u6574\u6570\u4e14\u6ee1\u8db3<\/p>\n\n\n\n
$$
\\frac{x}{y+z}+\\frac{y}{x+z}+\\frac{z}{x+y}=4
$$<\/p>\n\n\n\n
\u6c42\\(x,y,z\\).<\/p>\n\n\n\n
\u65b9\u7a0b\u4e24\u8fb9\u4e58\u4e0a\\((x+y)(x+z)(y+z)\\)\u53ef\u4ee5\u5f97\u5230\uff1a<\/p>\n\n\n\n
$$
x(x+y)(x+z)+y(x+y)(y+z)+z(x+z)(y+z)=4(x+y)(x+z)(y+z)
$$<\/p>\n\n\n\n
\u5c55\u5f00\u540e\u6574\u7406\u53ef\u5f97\uff1a<\/p>\n\n\n\n
$$
x^{3} – 3 x^{2} y – 3 x y^{2} + y^{3} – 3 x^{2} z – 5 x y z – 3 y^{2} z – 3 x z^{2} – 3 y z^{2} + z^{3}=0
$$<\/p>\n\n\n\n
\u4f7f\u7528sagemath\u7684EllipticCurve_from_cubic<\/code>\u65b9\u6cd5\u53ef\u4ee5\u5f97\u5230\uff1a<\/p>\n\n\n\n