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Solving Quadratic Equation (X-1)^2 = X-1
Published on April 12, 2025
Algebra
The equation (X-1)^2 = X-1 has two solutions, X = 1 and X = 2.
Question
Answer
The problem is to solve the equation
We can solve this equation step-by-step:
We can solve this equation step-by-step:
Step 1: Rewrite the equation.
Step 2: Move all terms to one side to set the equation to zero.
Step 3: Factor out the common term
Step 4: Simplify the expression inside the second parenthesis.
Step 5: Set each factor to zero to find the possible values of X.
Case 1:
Case 2:
Case 1:
Case 2:
The solutions to the equation are
Now letโs check the given options:
a) 3
b) 2
c) 0
a) 3
b) 2
c) 0
Comparing the solutions we found with the options, we see that option b) 2 is one of the solutions.
We can also verify the solutions by substituting them back into the original equation.
For
For
So,
For
So,
For
So,
For
So,
From the given options, only option b) 2 is a valid solution to the equation.
Final Answer: The final answer is