已知a^2-3a+1=0,求代数式3a分之2a^6-6a^4+2a^5-a^2-1的值

Question

已知a^2-3a+1=0,求代数式3a分之2a^6-6a^4+2a^5-a^2-1的值

Answer 1

解得a=(3±√5)/2
即a^2-3a+1=0
原式=2a^6-6a^4+2a^5-a^2-1/3a
=2a^4(a^2-3a+1)+8a^5-8a^4-a^2-1/3a
=8a^3(a^2-3a+1)+16a^4-8a^3-a^2-1/3a
=16a^2(a^2-3a+1)+40a^3-17a^2-1/3a
= 40a(a^2-3a+1)+103a^2-121a/3
=103(a^2-3a+1)+309a-121a/3-103
=806a/3-103
=300±(403√5)/2