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How do you identify extraneous solutions in radical equations?

In this lesson, you will learn how to identify extraneous solutions in radical equations. Through examples such as ( sqrt{x+2} = x - 7 ), you will practice checking for extraneous solutions by verifying potential solutions, like ( x = 5 ) and ( x = 10 ). We will also explore how to determine if a solution is extraneous by substituting it back into the original equation. Become proficient in recognizing when solutions are valid and when they are not, enhancing your mathematical problem-solving skills.

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How do you identify extraneous solutions in radical equations?

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  1. How do you identify extraneous solutions in radical equations? = x + 2

  2. In this lesson you will learn to determine if a radical equation has an extraneous solution by solving

  3. 5 is the radicand

  4. = -2

  5. = x -7 2 2 = x -7 x-1= x2 -14x + 49 x2 -15x + 50 = 0 x = 5, x = 10

  6. In this lesson you have learned to check for extraneous solutions by substitution

  7. =

  8. How would you solve the following equation? Be sure to identify any extraneous solutions. =3 -

  9. What would be an extraneous solution for the following equation? How do you know? • = x

  10. Solve for x; identify any extraneous solutions = Solve for x; identify any extraneous solutions - =2

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