证明不等式：x,y,z∈R,a,b,c∈R+,则x2(b+c)/a +y2(a+c)/b+z2(b+a)/c≧2(xy+yz+zx)
问题描述：
证明不等式：x,y,z∈R,a,b,c∈R+,则x2(b+c)/a +y2(a+c)/b+z2(b+a)/c≧2(xy+yz+zx)
答
原式左边两两配对：
x^2b/a+y^2a/b>=2xy
x^2c/a+z^2a/c>=2xz
y^2c/b+z^2b/c>=2yz
累加得证