已知x2-x-1=0,则x4+2x+1/x2=
问题描述:
已知x2-x-1=0,则x4+2x+1/x2=
答
x²-x-1=0x²=x+1x²-x-1=0x²-1=xx-1/x=1(x-1/x)²=1x²-2+1/x²=1x²+2+1/x²=5(x+1/x)²=5x+1/x=±√5x4+2x+1/x2=(x²+1/x)²=(x+1+1/x)²=(x+1/x+1)²...