%5E2%3D0.jpeg "(m-1)^2=0")
Solving the Equation (m-1)^2 = 0
The equation (m-1)^2 = 0 is a simple quadratic equation, which we can solve using the following steps:
Understanding the Equation
- Square root property: The equation states that the square of the expression (m-1) is equal to zero. This means that the expression itself must be zero.
- Factoring: We can also recognize that the equation is a perfect square trinomial, as it can be factored into (m-1)(m-1) = 0.
Solving for 'm'
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Take the square root: We can take the square root of both sides of the equation: √[(m-1)^2] = √0 m - 1 = 0
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Isolate 'm': Add 1 to both sides to isolate 'm': m - 1 + 1 = 0 + 1 m = 1
Solution and Verification
The solution to the equation (m-1)^2 = 0 is m = 1. We can verify this by substituting the value of m back into the original equation:
(1 - 1)^2 = 0 0^2 = 0
Therefore, the solution m = 1 satisfies the equation.
Conclusion
The equation (m-1)^2 = 0 has one solution, which is m = 1. This solution can be obtained using the square root property or by factoring the equation.