已知p+q+r=9,且p/(x^2-yz)=q/(y^2-zx)=r/(z^2-xy) ,则(px+qy+rz)/(x+y+z)等于?为什么能列出p/(x^2-yz)=q/(y^2-zx)=r/(z^2-xy)=(px+qy+rz)/(x^3+y^3+z^3-3xyz)?过程具体点.
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/30 20:39:59
![已知p+q+r=9,且p/(x^2-yz)=q/(y^2-zx)=r/(z^2-xy) ,则(px+qy+rz)/(x+y+z)等于?为什么能列出p/(x^2-yz)=q/(y^2-zx)=r/(z^2-xy)=(px+qy+rz)/(x^3+y^3+z^3-3xyz)?过程具体点.](/uploads/image/z/11467201-49-1.jpg?t=%E5%B7%B2%E7%9F%A5p%EF%BC%8Bq%EF%BC%8Br%EF%BC%9D9%2C%E4%B8%94p%2F%28x%5E2-yz%29%3Dq%2F%28y%5E2-zx%29%3Dr%2F%28z%5E2-xy%29+%2C%E5%88%99%28px%2Bqy%2Brz%29%2F%28x%2By%2Bz%29%E7%AD%89%E4%BA%8E%3F%E4%B8%BA%E4%BB%80%E4%B9%88%E8%83%BD%E5%88%97%E5%87%BAp%2F%28x%5E2-yz%29%3Dq%2F%28y%5E2-zx%29%3Dr%2F%28z%5E2-xy%29%3D%28px%2Bqy%2Brz%29%2F%28x%5E3%2By%5E3%2Bz%5E3-3xyz%29%3F%E8%BF%87%E7%A8%8B%E5%85%B7%E4%BD%93%E7%82%B9.)
已知p+q+r=9,且p/(x^2-yz)=q/(y^2-zx)=r/(z^2-xy) ,则(px+qy+rz)/(x+y+z)等于?为什么能列出p/(x^2-yz)=q/(y^2-zx)=r/(z^2-xy)=(px+qy+rz)/(x^3+y^3+z^3-3xyz)?过程具体点.
已知p+q+r=9,且p/(x^2-yz)=q/(y^2-zx)=r/(z^2-xy) ,则(px+qy+rz)/(x+y+z)等于?
为什么能列出p/(x^2-yz)=q/(y^2-zx)=r/(z^2-xy)=(px+qy+rz)/(x^3+y^3+z^3-3xyz)?过程具体点.
已知p+q+r=9,且p/(x^2-yz)=q/(y^2-zx)=r/(z^2-xy) ,则(px+qy+rz)/(x+y+z)等于?为什么能列出p/(x^2-yz)=q/(y^2-zx)=r/(z^2-xy)=(px+qy+rz)/(x^3+y^3+z^3-3xyz)?过程具体点.
p/(x^2-yz)=px/(x^3-xyz)分子、分母同乘x q/(y^2-zx)=qy/(y^3-yzx)分子、分母同乘y r/(z^2-xy)=rz/(z^3-zxy)分子、分母同乘z (a/b=c/d=(a+c)/(b+d)比例性质) 所以 p/(x^2-yz)=q/(y^2-zx)=r/(z^2-xy)=(px+qy+rz)/(x^3+y^3+z^3-3xyz) p/(x^2-yz)=(px+qy+rz)/(x^3+y^3+z^3-3xyz) q/(y^2-zx)=(px+qy+rz)/(x^3+y^3+z^3-3xyz) r/(z^2-xy)=(px+qy+rz)/(x^3+y^3+z^3-3xyz) p=(x^2-yz)(px+qy+rz)/(x^3+y^3+z^3-3xyz) q=(y^2-zx)(px+qy+rz)/(x^3+y^3+z^3-3xyz) r=(z^2-xy)(px+qy+rz)/(x^3+y^3+z^3-3xyz) p+q+r=(px+qy+rz)(x^2+y^2+z^2-xy-xz-yz)/x^3+y^3+z^3-3xyz=9 (x+y+z)(x^2+y^2+z^2-xy-xz-yz)=x^3+y^3+z^3-3xyz (px+qy+rz)/(x+y+z)=9