已知x-1/x=3,则X^4+1/X^4的值等于

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已知x-1/x=3,则X^4+1/X^4的值等于

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

x-1/x=3,则(x-1/x)^2=x^2+1/x^2-2=9,
所以,x^2+1/x^2=11,
等式两边再乘方,得x^4+1/x^4+2=112,
所以x^4+1/x^4=110