已知x2+3x+1=0,求(1)x+1/x,(2)x2+1/x2+2x+2/x的值
问题描述:
已知x2+3x+1=0,求(1)x+1/x,(2)x2+1/x2+2x+2/x的值
答
等式两边同除以x
x+3+1/x=0
x+1/x=-3
x²+1/x²+2x+2/x
=(x+1/x)²-2+2(x+1/x)
=(-3)²-2+2(-3)
=9-2-6
=1