Solve the following Radical Equation: \(\sqrt{x^3 - 4x^2 + 4x - 1} = x - 1\)
Answer
Step 6: Checking the solutions in the original equation: \(x = 0\) is not a solution, but \(x = 2\) and \(x = 3\) are solutions.
Step 1 ：Step 1: Squaring both sides to eliminate the square root: \((x - 1)^2 = x^3 - 4x^2 + 4x - 1\)
Step 2 ：Step 2: Simplifying the equation: \(x^2 - 2x + 1 = x^3 - 4x^2 + 4x - 1\)
Step 3 ：Step 3: Rearranging the equation: \(x^3 - 5x^2 + 6x = 0\)
Step 4 ：Step 4: Factoring the equation: \(x*(x - 2)*(x - 3) = 0\)
Step 5 ：Step 5: Setting each factor equal to zero and solving for x: \(x = 0\), \(x = 2\), \(x = 3\)
Step 6 ：Step 6: Checking the solutions in the original equation: \(x = 0\) is not a solution, but \(x = 2\) and \(x = 3\) are solutions.
