(x-1)^2+x^2+(x+1)^2+(x+2)^2=4x^2+4x+6
(2x+1)^2=4x^2+4x+1<4x^2+4x+6
(2x+2)^2=4x^2+8x+4
4x^2+8x+4-4x^2-4x-6=4x-2
因为x>=1
则4x-2>0
4x^2+4x+6<4x^2+8x+4=(2x+2)^2
(2x+1)^2<4x^2+4x+6<(2x+2)^2
则4x^2+4x+6不是平方数