1)
A>b>0,a^2>b^2>0
c>d>0
a^2c>b^2d>0
2)
(a^2+b^2+2)-2(a+b)
=(a^2-2a+1)+(b^2-2b+1)
=(a-1)^2+(b-1)^2
≥0
(a^2+b^2+2)≥2(a+b)