a2+3a=1,b2+3b=1.求 b/ a2+a/ b2的值 .

a²+3a=1 b²+3b=1
a、b是方程x²+3x-1=0的两根.由韦达定理得
a+b=-3
ab=-1
b/a²+a/b²
=(b³+a³)/(ab)²
=[(a+b)(a²-ab+b²)]/(ab)²
=(a+b)[(a+b)²-3ab]/(ab)²
=(-3)×[(-3)²-3×(-1)]/(-1)²
=-3×(9+3)/1
=-3×12
=-36