x+y+z=0,求x(1/y+1/z)+y(1/x+1/z)+z(1/x+1/y)+3

来源：学生作业帮编辑：搜搜做题作业网作业帮分类：数学作业时间：2024/05/14 14:35:34

x(1/y+1/z)+y(1/x+1/z)+z(1/x+1/y)+3
=x/y+x/z+y/x+y/z+z/x+z/y+3
=1/x(y+z)+1/y(x+z)+1/z(x+y)+3
又∵x+y+z=0
∴x+y=-z
x+z=-y
y+z=-x
∴1/x(y+z)+1/y(x+z)+1/z(x+y)+3
=1/x(-x)+1/y(-y)+1/z(-z)+3
=-1-1-1+3
=0
∴x(1/y+1/z)+y(1/x+1/z)+z(1/x+1/y)+3=0

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