已知a^2=3a-1,则2a^5-5a^4+2a^3-8a^2/a^2+1的值为?

题目

已知a^2=3a-1,则2a^5-5a^4+2a^3-8a^2/a^2+1的值为?

答案

2a^5-5a^4+2a^3-8a^2/a^2+1
=2a^5-5a^4+2a^3-8a+1
=a^2(2a^3-5a^2+2a)-8a+1
=(3a-1)[2a(3a-1)-5(3a-1)^2+2a(3a-1)]-8a+1
=(3a-1)[6a^2-2a-5(9a^2-6a+1)+6a^2-2a]-8a+1
=(3a-1)[18a-6-2a-45a^2+30a-5+18a-6-2a]-8a+1
=(3a-1)[62a-135a+45-17]-8a+1
=(3a-1)[-73a+28｝-8a+1
=-219a^2+73a+84a-28-8a+1
=149a-219(2a-1)-27
=149a-538a+219-27
=-390a+192