已知:x十y十z=0,且x,y,z均不为零,求证根号下1⼀x^2+1⼀y^2十1⼀z^2=|1⼀

十1/y+1/
2025-05-21 10:58:07
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回答(1):

证:(x+y+z)^2=x^2+y^2+z^2+2(xy+yz+zx)=0
x^2+y^2+z^2=-2(xy+yz+zx)
|1/x+1/y+1/z=|(xy+yz+zx)/xyz|
=|(x^2+y^2+z^2)/2xyz|