10 6 Radical Equations and Problem Solving 1
10. 6 Radical Equations and Problem Solving 1. Use the power rule to solve radical equations.
Not 4 x 2 + 9 !
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. It does not say that all solutions of the new equation are solutions of the original 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.
Solve: or r ea atic? n i L r ad u q Check: True
Solve: Check: or r ea atic? n i L r ad u q True
Solve: Square root will never be negative!
Solve: Check: or r ea atic? n i L r ad u q True
Solve: Rewrite and Foil! or r ea atic? n i L r ad u q Check: x = -1 True Check: x = -2 True
Solve: Check: y = 2 False r ro ? a e ic Lin drat a qu Extraneous Solution Check: y = 12 True
Solve: Check: True
Solve. a) 6 b) 8 c) 9 d) no solution Copyright © 2011 Pearson Education, Inc. Slide 10 - 13
Solve. a) 6 b) 8 c) 9 d) no solution Copyright © 2011 Pearson Education, Inc. Slide 10 - 14
Solve. a) 3, 4 b) 3 c) 4 d) no real-number solution Copyright © 2011 Pearson Education, Inc. Slide 10 - 15
Solve. a) 3, 4 b) 3 c) 4 d) no real-number solution Copyright © 2011 Pearson Education, Inc. Slide 10 - 16
- Slides: 16
