已知x²-4x+1=0,求x²+x负二次幂与x四次幂+x负四次幂的值

问题描述:

已知x²-4x+1=0,求x²+x负二次幂与x四次幂+x负四次幂的值

答:
x²-4x+1=0
两边同除以x得:
x-4+1/x=0
x+1/x=4
所以:
x²+x^(-2)
=x²+1/x²
=(x+1/x)²-2
=4²-2
=14
x^4+x^(-4)
=x^4+1/x^4
=(x²+1/x²)-2
=14²-2
=194