x,y,z为正实数,则( z^2-x^2)/(x+y)+(x^2-y^2)/(y+z)+(y^2-z^2)/(z+x)的最小值是急_数学解答

x,y,z为正实数,则( z^2-x^2)/(x+y)+(x^2-y^2)/(y+z)+(y^2-z^2)/(z+x)的最小值是
急用,谢谢

人气：402 ℃　时间：2020-08-16 06:31:18

解答

设x≥y≥z所以x^2≥y^2≥z^2≥01/(y+z)≥1/(x+z)≥1/(x+y)所以x^2/(x+y)+y^2/(y+z)+z^2/(x+z)(乱序和)≤x^2/(y+z)+y^2/(x+z)+z^2/(x+y)(顺序和)左边的移到右边去[x^2/(y+z)-y^2/(y+z)]+[y^2/(x+z)-z^2/(x+z)]+[z^2/(...