Question

已知方程2x^2+3x-1=0的两根为x1,x2,不解方程求:(1)1/x1+1/x2,(2)x1+x2

Answer 1

韦达定理
x1+x2=-3/2,x1x2=-1/2

Answer 2

2x²+3x-1=0
所以x1+x2=-3/2
x1x2=-1/2
所以
1/x1+1/x2
=(x1+x2)/x1x2
=(-3/2)/(-1/2)
=3

x1+x2=-3/2