已知x,y,z∈R,a,b,c∈R+,求证(b+c)/ax^2+(c+a)/by^2+(a+b)/cz^2 ≥2(xy+yz+zx)要过程
人气:434 ℃ 时间:2020-04-14 14:46:14
解答
b/ax^2+ a/by^2≥2√(x^2 y^2)=2|xy|≥2xy,
同理:c/ax^2+ a/cz^2≥2xz,
c/by^2+ b/cz^2≥2yz,
以上三个不等式相加可得所要证的不等式.
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