Solving Radical Equations and Inequalities

1. Solving Radical Equations and Inequalities Section 5.8

2. Radical Equations • Contains variable within a radical • Review: How did you solve • To Solve: • Isolate the radical • Raise both sides to a power that is equal to the index of the radical • Simplify and solve • If there are 2 radicals, set up the equation so only 1 radical is on each side of the equation

3. EX: Solve each equation • 1) 2) • 3) 4) • 5)

4. Extraneous Solutions • When raising both sides of an equation to an even power, you have to check your answers because you may get extraneous solutions. • EX: Solve. Check your solutions. • 1) 2)

5. Rational Exponents • Recall: • Therefore, when you see expressions raised to rational exponents in an equation, you can solve them using similar methods as you used for solving radical equations. • Raise both sides of equation to reciprocal power of given exponent • OR rewrite equation as radical equation and solve like previous problems • EX: Solve • 1) 2) • 3)

6. Radical Inequality • Inequality that contains variable within radical • Solve by using a graph & table OR algebraically • Similar to 5.5 notes • Graph & Table: • Look for where Y1 = Y2 and ERROR • Algebra: • Solve Inequality • Consider Radicand • If even index, radicand cannot be negative

7. EX: Solve • Solve algebraically AND graphically. • 1) 2)

8. Application • The time t in seconds that it takes a car to travel a quarter mile when starting from a full stop can be estimated by using the formula , where w is the weight of the car in pounds and p is the power delivered by the engine in horsepower. If the quarter-mile time for a 3590 lb car is 13.4 s, how much power does its engine deliver? Round to the nearest horsepower.

9. Homework • Pages 381-383 #27-49, 51, 58, 59, 60, 62-65