The -number of solutions of the equation `cos(pisqrt(x-4)cos(pi sqrtx)=1` is

Explanation

To solve the equation \( \cos(\pi \sqrt{x-4}) \cos(\pi \sqrt{x}) = 1 \), we need to analyze the conditions under which the product of the two cosine functions equals 1.

### Step-by-Step Solution:

1. **Understanding the Cosine Function**:
The cosine function \( \cos(\theta) \) equals 1 when \( \theta = 2n\pi \) for any integer \( n \). Therefore, for the product \( \cos(\pi \sqrt{x-4}) \cos(\pi \sqrt{x}) = 1 \) to hold, both cosine terms must equal 1.

2. **Setting Up the Equations**:
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