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# The number of solutions of the equation $\cos \left( {\pi \sqrt {x - 4} } \right) \cdot \cos \left( {\pi \sqrt x } \right) = 1$ is${\text{A}}{\text{. 1}} \\ {\text{B}}{\text{. 2}} \\ {\text{C}}{\text{. More than two}} \\ {\text{D}}{\text{. None of these}} \\$

Last updated date: 18th Mar 2023
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Hint: In this question we have to find the number of solutions of the given equation. To solve this question the main point is that the value of $\cos x$ is less than or equal to 1. At $x=0$ the value of cos is always to be 1.

In this question we have been given the equation $\cos \left( {\pi \sqrt {x - 4} } \right) \cdot \cos \left( {\pi \sqrt x } \right) = 1$
So, $\cos \left( {\pi \sqrt {x - 4} } \right) = 1$ and $\cos \left( {\pi \sqrt x } \right) = 1$
$\Rightarrow \sqrt {x - 4} = 0$ and $\sqrt x = 0$
$\Rightarrow x = 4{\text{ and }}x = 0$