Question

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

• A. -1
• B. 0
• C. 1
• D. 2

Answer 1

The correct option is B 0

$x=y\cos 2\pi /3=z\cos 4\pi /3$

$=-y\cos \pi /3=z(-\cos \pi /3)$

$x=-y/2=-z/2$

$\Rightarrow y=-2x,z=-2x$

$xy+yz+zx$

$=x(-2x)+(-2x)(-2x)+(-2x)x$

$=-2x^2+4a^2-2x^2$

$=0$