已知实数a,b满足ab=1,a+b=3,求a的四次方-b的四次方的值.

已知实数a,b满足ab=1,a+b=3
a²+b²=(a+b)²-2ab=9-2=7;
(a-b)²=(a+b)²-4ab=9-4=5;
a-b=±√5;
a的四次方-b的四次方
=(a²+b²)(a²-b²)
=(a²+b²)(a+b)(a-b)
=7×3×(±√5)
=±21√5;