问题 填空题 已知a+1a=8,则a4+a2+1a2=______. 答案 由题意,a+1a=8,故可得a2+2+1a2=64,即a2+1a2=62,a4+a2+1a2=a2+1a2+1=62+1=63.故答案为:63.