1.3. Given \( (x-3)^{\frac{2}{2}}=p^{2}-4 \) 1.3.1. Determine the values of P for whi

To solve the equation \( (x-3)^{1} = p^{2} - 4 \), we can simplify it to \( x - 3 = p^{2} - 4 \). We can then rearrange this to find \( p^{2} = x - 3 + 4 = x + 1 \). We now have \( p = \pm \sqrt{x + 1} \). This means that for every value of \( x \) greater than or equal to -1, there will be corresponding values of \( p \). In terms of specific values: - If \( x = -1 \), then \( p = 0 \). - If \( x = 0 \), then \( p = \pm 1 \). - If \( x = 3 \), then \( p = \pm 2 \). This tells us that \( p \) can take multiple values based on different choices of \( x \) within the specified domain!