Question

已知:a的平方加a+1分之a,=6分之1,则a的4次方加上a的平方加1分之a的平方=

Answer 1

已知,a/(a^2+a+1) = 1/6 ,
可得：(a^2+a+1)/a = 6 ,
即有：a+1+1/a = 6 ,
可得：a+1/a = 5 ,
所以,(a+1/a)^2 = 25 ,
即有：a^2+2+1/a^2 = 25 ,
可得：(a^4+a^2+1)/a^2 = a^2+1+1/a^2 = 24 ,
则有：a^2/(a^4+a^2+1) = 1/24 .