The sum of all real values of x satisfying the equation `(x^2-5x+5)^(x^2+4x-60)=1` is: (1) 3 (2) `-4` (3) 6 (4) 5

Explanation

To solve the equation \((x^2 - 5x + 5)^{(x^2 + 4x - 60)} = 1\), we can use the properties of exponents. The equation holds true under certain conditions. Specifically, if \(a^b = 1\), then either:

1. \(a = 1\) (for any \(b\))
2. \(a = -1\) (for even \(b\))
3. \(a = 0\) (for \(b > 0\))
4. \(b = 0\) (for \(a \neq 0\))

We will analyze each case one by one.
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