a+1/a=3
(a+1/a)^2=a^2+2+1/a^2=9,a^2+1/a^2=9-2=7
(a^2+1/a^2)^2=a^4+2+1/a^4=49,a^4+1/a^4=49-2=47
补充:
又因为a^2+1/a^2=7,所以a^2-2-1/a^2=5,即(a-1/a)^2=5,a-1/a=√5
a+1/a=3
(a+1/a)^2=a^2+2+1/a^2=9,a^2+1/a^2=9-2=7
(a^2+1/a^2)^2=a^4+2+1/a^4=49,a^4+1/a^4=49-2=47
补充:
又因为a^2+1/a^2=7,所以a^2-2-1/a^2=5,即(a-1/a)^2=5,a-1/a=√5