Question

已知x,y是实数,比较x方+y方+1与xy+x+y的大小

Answer 1

2x^2+2y^2+2-2xy-2x-2y

=x^2-2xy+y^2+x^2-2x+1+y^2-2y+1

=(x-y)^2+(x-1)^2+(y-1)^2

≥0

2x^2+2y^2+2≥2xy+2x+2y

x^2+y^2+1≥xy+x+y