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 (square root, cube root, etc.). To solve these equations, one typically isolates the radical on one side and then squares both sides to eliminate the radical. This process can introduce extraneous solutions, so it's 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 where one rearranges the equation to get the variable alone on one side. In the context of radical equations, this often involves moving constants to the opposite side before squaring both sides. This step is crucial for simplifying the equation and making it easier to solve.
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Equations with Two Variables
Extraneous Solutions
Extraneous solutions are solutions that emerge from the algebraic manipulation of an equation but do not satisfy the original equation. When solving radical equations, squaring both sides can introduce these false solutions. Therefore, it is vital to substitute the proposed solutions back into the original equation to verify their validity.
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Categorizing Linear Equations