Question

若a是方程x²-3x+1=0的一个根,求2a²-5a-2+3/(a²+1)的值

Answer 1

∵a是方程x²-3x+1=0的一个根
∴a²-3a+1=0, 由此得：
2a²-5a-2=a-4，a²+1=3a
∴2a²-5a-2+3/(a²+1)
=a-4+3/(3a)
=(a²+1)/a - 4
=3a/a - 4
=-1

Answer 2

a是方程x²-3x+1=0的一个根
a²-3a+1=0
a²-3a=-1.....(1)
a²+1=3a...(2)
2a²-5a-2+3/(a²+1)
=2(a²-3a)+(a-2)+[3/(a²+1)]
=(a-4)+[3/(a²+1)]
=(a-4)+[3/(a²+1)]
=(a-4)+(1/a)
=(a²-4a+1)/a
=(-a)/a
=-1

Answer 3

已知a是方程x^2-3x+1＝0的根，
a^2-3a+1＝0
a^2=3a-1
2a^2-5a-2+3/(a^2+1)
=2(3a-1)-5a-2+3/(3a+1-1)
=6a-2-5a-2+3/(3a)
=a-4+1/a
=(a^2-4a+1)/a
=(3a-1-4a+1)/a
=(-a)/a
=-1