设x^4+2x^3+ax^2+bx+1=(x^2+cx+d)^2,展开,得
x^4+2x^3+ax^2+bx+1≡x^4+2cx^3+(c^2+2d)x^2+2cdx+d^2,所以
2=2c (1)
a=c^2+2d (2)
b=2cd (3)
1=d^2 (4)
解得,a=3,b=2或者a=-1,b=-2.