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Solving Radical Equations and Inequalities

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Solving Radical Equations and Inequalities

Section 5.8

- 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

- 1) 2)
- 3) 4)
- 5)

- 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)

- 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)

- 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

- Graph & Table:

- Solve algebraically AND graphically.
- 1) 2)

- 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.

- Pages 381-383 #27-49, 51, 58, 59, 60, 62-65