問4はコーシーシゅワルツの定理から、
(1+xy+xz)/(1+y+z)^2≧x/(x+y+z)
(1+yz+yx)/(1+z+x)^2≧y/(x+y+z)
(1+zx+zy)/(1+x+y)^2≧z/(x+y+z)
∴(1+xy+xz)/(1+y+z)^2+(1+yz+yx)/(1+z+x)^2+(1+zx+zy)/(1+x+y)^2≧1