分类：教育/科学-理工学科-数学
问题：不等式证明设x,y,z∈R+,满是:yz+zx+xy=1.求证( 
设x,y,z∈R+,满是:yz+zx+xy=1.求证 
(1+x^2)/yz+(1+y^2)/zx+(1+z^2)/xy≥12(x^2+y^2+z^2). 

回答：设x,y,z∈R+,满是:yz+zx+xy=1.求证 
(1+x^2)/yz+(1+y^2)/zx+(1+z^2)/xy≥12(x^2+y^2+z^2). 

证 ∑(1+x^2)/yz=∑(yz+zx+xy+x^2)/yz=∑(x+y)(x+z)/yz
<==> ∑yz*∑x(x+y)(x+z)≥12xyz∑x^2
<===> ∑x^4*(y+z)+∑x^3*(y^2+z^2)-9xyz∑x^2+5xyz∑yz≥0
<==> ∑x[2x^2+yz+2(y-z)^2]*(y-z)^2≥0