已知x,y,z满足x/(y+z)+y/(z+x)+z/(x+y)=1,求代数式x2/(y+z)+y2/(x+z)+z2/(x+y)的值、

题目

已知x,y,z满足x/(y+z)+y/(z+x)+z/(x+y)=1,求代数式x2/(y+z)+y2/(x+z)+z2/(x+y)的值、
2是平方

答案

x/(y+z)+y/(z+x)+z/(x+y)=1所以x/(y+z)=1-[y/(z+x)+z/(x+y)] y/(z+x)=1-[x/(y+z)+z/(x+y)] z/(x+y)=1-[x/(y+z)+y/(z+x)] x²/(y+z)+y²/(z+x)+z²/(x+y) =x*[x/(y+z)]+y*[y/(z+x)]+z*[z/(x+y)] =x*{1-[y...