Here are the essential concepts you must grasp in order to answer the question correctly.
Radical Equations
Radical equations are equations that involve a variable within a radical, typically a square root. To solve these equations, one common method is to isolate the radical on one side and then square both sides to eliminate the radical. However, squaring both sides can introduce extraneous solutions, so it is essential to check all proposed solutions in the original equation.
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Isolating the Variable
Isolating the variable is a fundamental algebraic technique used to solve equations. This involves rearranging the equation to get the variable on one side and all other terms on the opposite side. In the context of radical equations, isolating the radical before squaring is crucial to ensure accurate solutions and to simplify the solving process.
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Extraneous Solutions
Extraneous solutions are solutions that emerge from the process of solving an equation but do not satisfy the original equation. This often occurs when both sides of an equation are squared, as this can introduce additional solutions that are not valid. Therefore, it is important to substitute proposed solutions back into the original equation to verify their validity.
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