Question

已知x,y,z是实数,a,b,c是正实数,求证

Answer 1

[（b+c)/a]x^2 + [(a+c)/b]y^2 + [(a+b)/c]z^2

=(b/a)x^2+(a/b)y^2+(c/a)x^2+(a/c)z^2+(c/b)y^2+(b/c)z^2

>=2根号（（b/a)x^2 *(a/b)y^2)+2根号((c/a)x^2 *(a/c)z^2)+2根号((c/b)y^2* (b/c)z^2)

=2(xy+yz+xz)