解答：x^2+y^2=(x+y)^2-2xy=25-4=21(x-y)^2=(x+y)^2-4xy=25-8=17x^8+y^8=(x^4+y^4)^2-2x^4y^4=[(x^2+y^2)^2-2x^2y^2]^2-2(xy)^4={[(x+y)^2-2xy]^2-2(xy)^2]^2-2(xy)^4=(21^2-8)^2-2*16=187457
