a^2+b^2=(a+b)^2-2ab=1-2ab=2ab=-1/2所以方程x^2-x-1/2=0的解为a,b所以a^2=a+1/2b^2=b+1/2化简a^7=a(a^2)^3=a(a+1/2)^3=41/8a+15/8同理化简b^7=41/8b+15/8a^7+b^7=41/8(a+b)+15/8+15/8=71/8
