Question

已知a^2+a-1=0,则代数式a^4+2a^3-3a^2-4a+3的值是

Answer 1

a^2+a-1=0
a^2+a=1
a^4+2a^3-3a^2-4a+3
=a^4+a^3+a^3-3a^2-4a+3
=a^2(a^2+a)+a^3-3a^2-4a+3
=a^2+a^3-3a^2-4a+3
=a(a+a^2)-3a^2-4a+3
=a-3a^2-4a+3
=-3a^2-3a+3
=-3(a^2+a)+3
=-3+3
=0