Question

If the equation $2\cos x+\cos 2\lambda x=3$ has only one solution, then $\lambda$ is

• A. 1
• B. a rational number
• C. an irrational number
• D. None of these

Answer 1

The correct option is C an irrational number

$2co{s}^2\lambda x-1=3-2cosx2co{s}^2\lambda x+2cosx-4=0co{s}^2\lambda x+cosx-2=0$
$\therefore cosx=cos\lambda x=1\Rightarrow \lambda isirrational$