Solving radical equations and inequalities
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Solving Radical Equations and Inequalities. Section 5.8. 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

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Solving Radical Equations and Inequalities

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Solving radical equations and inequalities

Solving Radical Equations and Inequalities

Section 5.8


Radical equations

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


Ex solve each equation

EX: Solve each equation

  • 1) 2)

  • 3) 4)

  • 5)


Extraneous solutions

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)


Rational exponents

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)


Radical inequality

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


Ex solve

EX: Solve

  • Solve algebraically AND graphically.

  • 1) 2)


Application

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.


Homework

Homework

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


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