Question

If a = b $\cos \frac{2\mathrm{\pi }}{3}=c\cos \frac{4\mathrm{\pi }}{3}$, then write the value of ab + bc + ca.

Answer 1

$$\begin{gathered} a=b\cos 120°=c\cos 240° \\ \Rightarrow a=-\frac{1}{2}b=-\frac{1}{2}c \\ \mathrm{Therefore}, \\ ab+bc+ca=\frac{-1}{2}b\times b+b\times b+b\times \frac{-1}{2}b \\ =-b^2+b^2 \\ =0 \end{gathered}$$