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Published byAnnalise Hapgood Modified about 1 year ago

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CHAPTER 5 5-8 solving radical equations and inequalities

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OBJECTIVES Solve radical equations and inequalities.

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RADICAL A radical equation contains a variable within a radical. Recall that you can solve quadratic equations by taking the square root of both sides. Similarly, radical equations can be solved by raising both sides to a power.

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STEPS TO SOLVE

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EXAMPLE#1 Solve each equation.

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EXAMPLE#2 Solve each equation

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EXAMPLE Solve

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EXAMPLE Solve

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SOLVING RADICALS WITH EXTRANEOUS SOLUTIONS Raising each side of an equation to an even power may introduce extraneous solutions.

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EXAMPLE Solve Method 1 Use a graphing calculator. Let Y1 = and Y2 = 5 – x. The graphs intersect in only one point, so there is exactly one solution. The solution is x = – 1

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CONTINUE Method 2 Use algebra to solve the equation.

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EXAMPLE Solve

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EXAMPLE Solve

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SOLVING EQUATIONS WITH RATIONAL EXPONENTS Solve (5x + 7) = 3 1 3

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EXAMPLES Solve 2x = (4x + 8) 1 2

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EXAMPLE Solve (2x + 15) = x 1 2

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RADICAL INEQUALITIES A radical inequality is an inequality that contains a variable within a radical. You can solve radical inequalities by graphing or using algebra.

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EXAMPLE Solve. Method 1 Use a graph and a table. On a graphing calculator, let Y1 = and Y2 = 9. The graph of Y1 is at or below the graph of Y2 for values of x between 3 and 21. Notice that Y1 is undefined when < 3. The solution is 3 ≤ x ≤ 21.

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CONTINUE Method 2 Use algebra to solve the inequality.

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EXAMPLE Solve.

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APPLICATION The speed s in miles per hour that a car is traveling when it goes into a skid can be estimated by using the formula s =, where f is the coefficient of friction and d is the length of the skid marks in feet. A car skids to a stop on a street with a speed limit of 30 mi/h. The skid marks measure 35 ft, and the coefficient of friction was 0.7. Was the car speeding? Explain.

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STUDENT GUIDED PRACTICE Do even problems 2 -14 in your book page 380

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HOMEWORK Do even problems from 27-41 in your book page 381

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