已知a+1/a=3,求下列式子的值

题目

已知a+1/a=3,求下列式子的值
(1)a^2+1/a^2
(2)a^3+1/a^3
(3)a^4+1/a^4

答案

(1)a^2+1/a^2
=(a+1/a)^2-2
=9-2
=7
(2)a^3+1/a^3
=(a+1/a)(a^2-1+1/a^2)
=3*(7-1)
=18
(3)a^4+1/a^4
=(a^2+1/a^2)^2-2
=49-2
=47