两式相减：
x²+y²+2-(2x+2y)
=x²+y²+1+1-2x-2y
=x²-2x+1+y²-2y+1
=(x²-2x+1)+(y²-2y+1)
=(x-1)²+(y-1)²
∵(x-1)²≥0,(y-1)²≥0
∴(x-1)²+(y-1)²≥0
∴x²+y²+2-(2x+2y)≥0
∴x²+y²+2≥2x+2y.