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A solution that does not satisfy the original equation?
an extraneous solution.
Why is it necessary to check for extraneous solutions in radical equations?
1) When solving radical equations, it is often convenient to square both sides of the equation. 2) When doing this, extraneous solutions may be introduced - the new equation may have solutions that are not solutions of the original equation. Here is a simple example (without radicals): The equation x = 5 has exactly one solution (if you replace x with 5, the equation is true, for other values, it isn't). If you square both sides, you get: x2 = 25 which also has the solution x = 5. However, it also has the extraneous solution x = -5, which is not a solution to the original equation.
What are the steps to solving a radical equation?
Details may vary depending on the equation. Quite often, you have to square both sides of the equation, to get rid of the radical sign. It may be necessary to rearrange the equation before doing this, after doing this, or both. Squaring both sides of the equation may introduce "extraneous" roots (solutions), that is, solutions that are not part of the original equation, so you have to check each solution of the second equation, to see whether it is also a solution of the first equation.
What is A number that makes a equation true?
The solution set is the answers that make an equation true. So I would call it the solution.
What is the value of a variable that makes an equation true?
That's the "solution" of the equation.
