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 B a rational number

The maximum value of LHS is 3 and thus,

$2\cos x+\cos 2\lambda x=3$

$\Rightarrow$ $\cos x=1$ and $\cos 2\lambda x=1$

$\Rightarrow x=2n\pi$ and thus, $\lambda =\frac{n}{2}$

Hence option B seems correct.