已知实数ab满足a²+2a=2,b²+2b=2,求1/a+1/b

已知实数ab满足a²+2a=2,b²+2b=2,求1/a+1/b

a²+2a-2=0
b²+2b-2=0
所以a和b是方程x²+2x-2=0的根
所以a+b=-2
ab=-2
所以
1/a+1/b
=(a+b)/ab
=(-2)/(-2)
=1