Question

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+

Answer 1

/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.