The concept:
We are given the equation:
[tex]5^{x(x-1)} = 1[/tex]
Which can be simplified as:
[tex]5^{x^{2} - x} = 1^{1}[/tex]
Since any number to the power '0' is 1
x² - x must be equal to 0 for the given equation to be true
Solving for x:
x² - x = 0
x(x-1) = 0
now, we can divide both sides by either x OR x-1
So we will see what we get for either choice:
x = 0/(x-1) x-1 = 0/x
x = 0 x = 1
Hence, the value of x is either 0 or 1
