Question

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

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

Answer 1

a是方程x^2-3x+1=0的根,
则a^2-3a+1=0；
a^2-2a=a-1；a^2+1=3a。
则2a^2-5a-2+2/(a^2+1)
=2（a^2-2a）-（a+2）+2/(3a)
=2（a-1）-（a+2）+2/(3a)
=a-3+2/(3a)
=[3（a^2+1)-1]/(3a) -3
=(3*3a-1)/(3a) -3
=-1/(3a).

解方程x^2-3x+1=0得:x=a=(3±√5)/2;
则2a^2-5a-2+2/(a^2+1)=-1/(3a)=(-2/3)/(3±√5)
=(3±√5)/6.

Answer 2

a^2+1=3a,
a-4+2/(3a)=...=a/3

Answer 3

2a^2-5a-2+3/(a^2+1)=2a^2-6a+2+a-4+
3/(3a)=a
-4+
1/a=(a^2-4a+1)/a=-a/a=-1

Answer 4

求根公式把a求出来，再代一下