x+y=1,①x^2+y^2=2.②[①^2-②]/2,xy=-1/2,x^3+y^3=(x+y)(x^2-xy+y^2)=5/2,x^4+y^4=(x^2+y^2)^2-2(xy)^2=4-1/2=7/2,所以x^7+y^7=(x^3+y^3)(x^4+y^4)-(x+y)(xy)^3=35/4+1/8=71/8.
