Question

已知a^2-4a+1=0 求a+1/a的值 求(a^4+1)/a^2的值

Answer 1

已知a^2-4a+1=0,所以a-4+1/a=0，所以a+1/a=4；森唯因为(a+1/a)^2=16，颂春者所以a^2+2+1/a^2=16，所以野薯(a^4+1)/a^2=a^2+1/a^2=16-2=14

Answer 2

∵a²-4a+1=0 (a-2)²=3 a-2=±√3 a1=2+√3 a2=2-√3
当a=2+√3时，a+1/a=(2+√3)+1/(2+√3)=2+√3+(2-√3)=4
(a^4+1)/a²=a²+1/a²=(2+√3)²灶亮厅键则+1/(2+√3)²=14
当a=2-√3 a+1/a=(2-√3)+1/(2-√隐隐3)=4
(a^4+1)/a²=a²+1/a²=(2-√3)²+1/(2-√3)²=14

Answer 3

a+1/哗乎a=(a^2+1)/a=4a/a=4
a^4+1)/纤芦迟a^2=a^2+1/毁李a^2=(a+1/a)^2-2=4*4-2=14

Answer 4

a²-4a+1=（a-2）祥拿²=0 ∴ a=2
(a^4+1)/扒基a^2=（2^4+1）/2²=17/谨此搭4

Answer 5

a^2-4a+1=0
除派贺燃以a得 a-4+1/尘虚拍贺a=0
a+1/a=4
(a^4+1)/a^2
=a²+1/a²
=(a+1/a)²-2
=4²-2
=14

追问

为什么还要-2

追答

a²+1/a²
=a²+2×a×1/a+1/a²-2×a×1/a
=(a+1/a)²-2