Radical Equations and Problem Solving 10.6 1.Use the power rule to solve radical equations.

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Presentation transcript:

Radical Equations and Problem Solving Use the power rule to solve radical equations.

Not 4x !

To Solve Equations: Inverse Operations Add ↔ Subtract Multiply ↔ Divide Powers ↔ Roots

Radical Equations Power Rule If both sides of an equation are raised to the same power, all solutions of the original equation are also solutions of the new equation. Extraneous Solution Check all solutions!

Radical Equations To Solve Radical Equations 1.Isolate the radical. 2. Raise both sides of the equation to the same power as the index. 3. Linear or Quadratic? Solve. (Repeat 1 & 2 if necessary) 4. Check.

Linear or quadratic? Solve: Check: True

Linear or quadratic? Solve: Check: True

Solve: Square root will never be negative!

Solve: Check: Linear or quadratic? True

Solve: Check: x = -1 Linear or quadratic? True Check: x = -2 True Rewrite and Foil!

Solve: Linear or quadratic? Check: y = 2 True Check: y = 12 False Extraneous Solution

Solve: Check: True

Slide Copyright © 2011 Pearson Education, Inc. Solve. d) no solution a) 6 b) 8 c) 9

Slide Copyright © 2011 Pearson Education, Inc. Solve. d) no solution a) 6 b) 8 c) 9

Slide Copyright © 2011 Pearson Education, Inc. Solve. d) no real-number solution a)  3, 4 b)  3 c) 4

Slide Copyright © 2011 Pearson Education, Inc. Solve. d) no real-number solution a)  3, 4 b)  3 c) 4