Question

The number of the solutions of thc equation $\cos \left(\pi \sqrt{x-4}\right)\cos \left(\pi \sqrt{x}\right)=1$ is

• A. $>2$
• B. $2$
• C. $1$
• D. $0$

Answer 1

Answer: (C)

$1$

the above is possible only and only when
$\cos \left(\pi \sqrt{x-4}\right)=\cos \left(\pi \sqrt{x}\right)=1$ or $-1$
clearly $x=4$ is the only solution