Question

Cho a,b,c khác 0 thỏa mãn \(a\left(\dfrac{1}{b}+\dfrac{1}{c}\right)+b\left(\dfrac{1}{c}+\dfrac{1}{a}\right)+c\left(\dfrac{1}{a}+\dfrac{1}{b}\right)=-2\)

và a³+b³+c³=1. CMR  \(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=1\)