因为,（a + 1/a）^2 = a^2 + 2 + 1/a^2 = 5^2 ,
所以,a^2 + 1/a^2 = 5^2 - 2 = 23 .
因为,（a^2 + 1/a^2）^2 = a^4 + 2 + 1/a^4 = 23^2 ,
所以,a^4 + 1/a^4 = 23^2 - 2 = 527 .