Question

若a的平方+a=-1,则a的4次方+2a的3次方-3a的2次方-4a+3的值为?

Answer 1

a^2+a=-1

=>a^2+a+1=0

a^4+2a^3-3a^2-4a+3

=(a^4+a^3+a^2)+(a^3+a^2+a)-(5a^2+5a+5)+8

=a^3(a^2+a+1)+a^2(a^2+a+1)-5(a^2+a+1)+8

=0+0+0+8

=8