一,
(3^2+1)(3^4+1)(3^8+1)(3^16+1)
=(3^2-1)(3^2+1)(3^4+1)(3^8+1)(3^16+1)/(3^2-1)
=(3^4-1)(3^4+1)(3^8+1)(3^16+1)/(3^2-1)
=(3^8-1)(3^8+1)(3^16+1)/(3^2-1)
=(3^16-1)(3^16+1)/(3^2-1)
=(3^32-1)/(3^2-1)
=(3^32-1)/8
二,
x^2+y^2+4x-6y+13=0
x^2+4x+4+y^2-6y+9=0
(x+2)^2+(y-3)^2=0
x=-2
y=3
x+y=1
三,
x^3+2x^2+3
=X^3+X^2-X+X^2+X+3
=X(X^2+X-1)+X^2+X+3
因为x^2+x-1=0 X^2+X=1
所以X(X^2+X-1)+X^2+X+3
=0+1+3
=4
即原式=4