1. Tardigrade
  2. Question
  3. Mathematics
  4. If x=y cos (2π /3)=z cos (4π /3), then xy+yz+zx is equal to

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

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

Bihar CECEBihar CECE 2015

Solution:

We have, $ x=y\cos \frac{2\pi }{3}=z\cos \frac{4\pi }{3}0 $ $ \Rightarrow $ $ x=\frac{-y}{2}=-\frac{z}{2} $ $ \Rightarrow $ $ \frac{x}{1}=\frac{y}{-2}=\frac{z}{-2}=\lambda $ [say] $ \Rightarrow $ $ x=\lambda ,y=-2\lambda ,z=-2\lambda $ $ \Rightarrow $ $ xy+yz+zx=-2{{\lambda }^{2}}+4{{\lambda }^{2}}-2{{\lambda }^{2}}=0 $