分式问题3

已知A+A分之1=5,则A的平方分之A的4次方+A的2次方+1的值是多少
2025-01-02 01:44:26
推荐回答(3个)
回答1:

A+1/A=5
(A+1/A)^2=A^2+1/A^2+2=25
所以A^2+1/A^2=23
(A^4+A^2+1)/A^2=A^2+1/A^2+1=23+1=24

回答2:

a+1/a=5

(a^4+a^2+1)/a^2
=a^2+1/a^2+1
=(a+1/a)^2-1
=5^2-1
=24

回答3:

a+1/a=5

(aaaa+aa+1)/aa
=aa+1+1/aa
=(a+1/a)^2-1
=5^2-1
=24