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10.6 Solving Equations with Radicals

10.6 Solving Equations with Radicals. Objective 1 . Solve radical equations by using the power rule. Slide 10.6- 2. When the power rule is used to solve an equation, every solution of the new equation must be checked in the original equation .

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10.6 Solving Equations with Radicals

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  1. 10.6 Solving Equations with Radicals

  2. Objective 1 Solve radical equations by using the power rule. Slide 10.6- 2

  3. When the power rule is used to solve an equation, every solution of the new equation must be checked in the original equation. Solve radical equations by using the power rule. The power rule does not say that all solutions of the new equation are solutions of the original equation. They may or may not be. Solutions that do not satisfy the original equation are called extraneous solutions. They must be rejected. Slide 10.6- 3

  4. CLASSROOM EXAMPLE 1 Using the Power Rule Check: Solution: Solve True Since 3 satisfies the original equation, the solution set is {3}. Slide 10.6- 4

  5. Solve radical equations by using the power rule. Slide 10.6- 5

  6. CLASSROOM EXAMPLE 2 Using the Power Rule Solution: Solve The equation has no solution, because the square root of a real number must be nonnegative. The solution set is . Slide 10.6- 6

  7. Objective 2 Solve radical equations that require additional steps. Slide 10.6- 7

  8. CLASSROOM EXAMPLE 3 Using the Power Rule (Squaring a Binomial) Solution: Solve Step 1The radical is alone on the left side of the equation. Step 2Square both sides. Step 3The new equation is quadratic, so get 0 on one side. Slide 10.6- 8

  9. CLASSROOM EXAMPLE 3 Using the Power Rule (Squaring a Binomial) (cont’d) Step 4Check each proposed solution in the original equation. False True The solution set is {1}. The other proposed solution, – 4, is extraneous. Slide 10.6- 9

  10. CLASSROOM EXAMPLE 4 Using the Power Rule (Squaring a Binomial) Solution: Solve Step 1The radical is alone on the left side of the equation. Step 2Square both sides. Step 3The new equation is quadratic, so get 0 on one side. Slide 10.6- 10

  11. CLASSROOM EXAMPLE 4 Using the Power Rule (Squaring a Binomial) (cont’d) Step 4Check each proposed solution in the original equation. False True The solution set of the original equation is {0}. Slide 10.6- 11

  12. CLASSROOM EXAMPLE 5 Using the Power Rule (Squaring Twice) Solution: Solve Square both sides. Isolate the remaining radical. Square both sides. Apply the exponent rule (ab)2 = a2b2. Slide 10.6- 12

  13. CLASSROOM EXAMPLE 5 Using the Power Rule (Squaring Twice) (cont’d) Check: x = 3 False Check: x =  1 The solution set is { 1}. True Slide 10.6- 13

  14. Objective 3 Solve radical equations with indexes greater than 2. Slide 10.6- 14

  15. CLASSROOM EXAMPLE 6 Using the Power Rule for a Power Greater Than 2 Solution: Solve Cube both sides. Check: The solution set is {9}. True Slide 10.6- 15

  16. Objective 4 Use the power rule to solve a formula for a specified variable. Slide 10.6- 16

  17. CLASSROOM EXAMPLE 7 Solving a Formula from Electronics for a Variable Solve the formula for R. Solution: Slide 10.6- 17

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