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Solve radical equations and inequalities. PowerPoint PPT Presentation


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Objective. Solve radical equations and inequalities. SOLVING RADICAL EQUATIONS: #1: _______ the _______ #2: Raise both sides to the _________ of the ________. Example 1: Solving Equations Containing One Radical. Solve each equation. Check your answer on your calculator. A. B. C.

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Solve radical equations and inequalities.

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Solve radical equations and inequalities

Objective

Solve radical equations and inequalities.

SOLVING RADICAL EQUATIONS:

#1: _______ the _______

#2: Raise both sides to the _________ of the ________.

Example 1: Solving Equations Containing One Radical

Solve each equation. Check your answer on your calculator.

A.

B.

C.


Solve radical equations and inequalities

Example 2: Solving Equations Containing Two Radicals

Solve and check your answer on your calculator.

A.

B.

C.


Solve radical equations and inequalities

Raising each side of an equation to an even power may

introduce ______________ solutions.

Example 3: Solving Equations with Extraneous Solutions

A. Solve

Method 1 Use a graphing calculator.

Method 2 Use algebra to solve the equation.

B. Solve the equation.

Method 1 Use a graphing calculator.

Method 2 Use algebra to solve the equation.


Solve radical equations and inequalities

1

2

2x = (4x + 8)

1

1

3

3

C. (x + 5) = 3

(5x + 7) = 3

C. Solve.

Example 4: Solving Equations with Rational Exponents

Solve each equation.

A.

B.


Solve radical equations and inequalities

A. Solve. .

30

fd

Example 5: Solving Radical Inequalities

Method 1 Use a graph and a table.

Method 2 Use algebra to solve the inequality.

B. Solve.

Method 1 Use a graph and a table.

Method 2 Use algebra to solve the inequality.

Example 6: 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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