已知x-1/x=3,则X^4＋1/X^4的值等于

题目

已知x-1/x=3,则X^4＋1/X^4的值等于

答案

x^4+1/x^4
=(x²+1/x²)²-2
=[(x-1/x)²+2]²-2
=[(x-1/x)²+2]²-2
=[3²+2]²-2
=121-2
=119