Question

已知a是方程x^2-3x+1=0的根,求2a^2-5a-2+3/(a^2+1)的值

Answer 1

a是方程x^2-3x+1=0的根

a^2-3a+1=0

所以a^2-3a=-1

且a^2+1=3a

所以

2a^2-5a-2+3/(a^2+1)

=2a^2-6a+a-2+3/(3a)

=2(a^2-3a)+a-2+1/a

=2*(-1)+a-2+1/a

=a-3+1/a

=(a^2-3a+1)/a

=0/a

=0