Question

9.已知 a+b+c=2023,a/(x^2-y=b/(y^2-xz)=c/(z^2-xy),x+y+z0,2k(ax+by+c)/(x+y

Answer 1

问：9.已知 a+b+c=2023,a/(x^2-y=b/(y^2-xz)=c/(z^2-xy),x+y+z0,2k(ax+by+c)/(x+y

答：a/(x2-yz)=b/(y2-zx)=c/(x2-xy) ＝ k (1)利用合分比(a+b+c) / (x^2+y^2+c^2-xy-yz-xz) = k (2) (1)左边分别在分子，分母乘以a,b,c得ax/x^3-xyz=by/(y^3-xyz)=cz/(x^3-xyz) = k利用合分比=(ax+by+cz) / (x^3+y^3+z^3-3xyz) = k由于x^3+y^3+z^3-3xyz = (x+y+z)(x^2+y^2+c^2-xy-yz-xz) = (x+y+z) * (a+b+c)/k 将（2）代入所以ax+by+cz = k(x^3+y^3+z^3-3xyz) = k (x+y+z)(a+b+c) / k = (x+y+z)(a+b+c)