(x-3)(x-4)%3D(x-2)(x-3)(x-5).jpeg "(x-2)(x-3)(x-4)=(x-2)(x-3)(x-5)")
Solving the Equation: (x-2)(x-3)(x-4) = (x-2)(x-3)(x-5)
This equation presents a straightforward algebraic problem, and we can solve it by using the properties of multiplication and equality.
Understanding the Problem
The equation is a polynomial equation. It involves products of linear factors, which are expressions of the form (x-a), where 'a' is a constant.
Our goal is to find the values of 'x' that make the equation true.
Solving the Equation
-
Simplify: The first step is to simplify the equation. Since both sides have common factors, we can divide both sides by (x-2)(x-3):
(x-2)(x-3)(x-4) / (x-2)(x-3) = (x-2)(x-3)(x-5) / (x-2)(x-3)
This leaves us with: (x-4) = (x-5)
-
Solve for x: Now we have a simple linear equation. Subtracting 'x' from both sides gives: -4 = -5
-
Analyze the result: The equation -4 = -5 is false. This means there is no solution to the original equation.
Conclusion
The equation (x-2)(x-3)(x-4) = (x-2)(x-3)(x-5) has no solutions. This is because the simplification process leads to a contradiction, indicating that there is no value of 'x' that can satisfy the initial equation.