Here are the essential concepts you must grasp in order to answer the question correctly.
Radical Equations
Radical equations are equations in which a variable is contained 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 important to check all potential solutions in the original equation.
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Isolating the Variable
Isolating the variable involves rearranging the equation to get the variable alone on one side. This is a crucial step in solving equations, especially in radical equations, as it allows for the application of inverse operations, such as squaring both sides to eliminate the radical. Proper isolation simplifies the equation and makes it easier to solve.
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Equations with Two Variables
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 squaring both sides of a radical equation. It is essential to substitute any found solutions back into the original equation to verify their validity and ensure they are not extraneous.
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Categorizing Linear Equations