已知x+1/y=z+1/x=1,求y+1/z的值..
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已知x+1/y=z+1/x=1,求y+1/z的值..已知x+1/y=z+1/x=1,求y+1/z的值..已知x+1/y=z+1/x=1,求y+1/z的值..x+1/y=z+1/x=1y=1/(1-x)
已知x+1/y=z+1/x=1,求y+1/z的值..
已知x+1/y=z+1/x=1,求y+1/z的值..
已知x+1/y=z+1/x=1,求y+1/z的值..
x+1/y=z+1/x=1
y=1/(1-x)
z=1-1/x=(x-1)/x
y+1/z=1/(1-x)+x/(x-1)=1/(1-x)-x/(1-x)=(1-x)/(1-x)=1
答案是1
由x+1/y=1可得y=1/(1-x)
由z+1/x=1可得1/z=x/(x-1)
所以 y+1/z=(1-x)/ (1-x)=1
因为x+1/y=z+1/x=1,所以y=1/(1-x),z=1-1/x y+1/z=1/(1-x)+1/(1-1/x)=1/(1-x)+x/(x-1)=1
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