Question

If $x=y\cos \frac{2\pi }{3}=z\cos \frac{4\pi }{3}$ then xy + yz + zx is equal to

• A. $-1$
• B. $0$
• C. $1$
• D. $2$

Answer 1

The correct option is B $0$

Given, $x=y\cos \frac{2\pi }{3}=z\cos \frac{4\pi }{3}$
$x=\frac{-y}{2}=\frac{-z}{2}$
Thus, $xy+yz+zx=x(-2x)+(-2x)(-2x)+(-2x)\left(x\right)$
= $-2x^2+4x^2-2x^2$
= $0$