Download 171S3.4 Solving Rational Equations and Radical Equations

171S3.4 Solving Rational Equations and Radical Equations
MAT 171 Precalculus Algebra
Dr. Claude Moore
Cape Fear Community College
CHAPTER 3: Quadratic Functions and Equations; Inequalities
3.1
3.2
3.3
3.4
3.5
The Complex Numbers
Quadratic Equations, Functions, Zeros, and Models
Analyzing Graphs of Quadratic Functions
Solving Rational Equations and Radical Equations
Solving Equations and Inequalities with Absolute Value
Go to SAS Curriculum Pathways, use Subscriber Login and User name: able7oxygen. Explore rational functions and radical functions by using Quick Launch # 1214 at http://www.sascurriculumpathways.com/ 3.4 Solving Rational Equations
and Radical Equations
• Solve rational equations.
• Solve radical equations.
February 24, 2011
Some Media for this Section
1. Solving Rational Equations 1 solving simple equations with algebraic fractions. http://cfcc.edu/faculty/cmoore/RationalEquations1.wmv
2. Solving Rational Equations 2 solving more complex equations with algebraic fractions. http://cfcc.edu/faculty/cmoore/RationalEquations2.wmv
3. Solving Radical Equations solving equations with square roots. http://cfcc.edu/faculty/cmoore/SquareRootEquations1.wmv
Watch this very good (9­min) video on solving rational equations. http://www.youtube.com/watch?v=vKakDNh6Q3k
Example
Solve:
Solution: Multiply both sides by the LCD 6.
Rational Equations ­ Equations containing rational expressions are called rational equations.
Solving such equations requires multiplying both sides by the least common denominator (LCD) to clear the equation of fractions.
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171S3.4 Solving Rational Equations and Radical Equations
Example (continued)
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Example
The possible solution is 5.
Solve:
Solution: Multiply both sides by the LCD x ­ 3.
TRUE
The solution is 5. Radical Equations
Example (continued)
A radical equation is an equation in which variables appear in one or more radicands. For example:
The possible solutions are –3 and 3.
Check x = 3:
Check x = –3:
The Principle of Powers
For any positive integer n:
If a = b is true, then an = bn is true.
TRUE
The number ­3 checks, so it is a solution.
Not Defined
Division by 0 is not defined, so 3 is not a solution.
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171S3.4 Solving Rational Equations and Radical Equations
Solving Radical Equations
To solve a radical equation we must first isolate the radical on one side of the equation.
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Example
Solve
Check x = 5:
Solution
Then apply the Principle of Powers.
When a radical equation has two radical terms on one side, we isolate one of them and then use the principle of powers. If, after doing so, a radical terms remains, we repeat these steps.
TRUE
The solution is 5.
Example
Example (continued)
Solve: The possible solutions are 9 and 2.
Solution: First, isolate the radical on one side.
Check x = 2.
Check x = 9.
TRUE
FALSE
Since 9 checks but 2 does not, the only solution is 9.
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171S3.4 Solving Rational Equations and Radical Equations
Example
Solve: February 24, 2011
Example (continued)
We check the possible solution, 4, on a graphing calculator.
Graph the two functions and find point of intersection.
Solution: Since y1= y2 when x = 4, the number 4 checks. It is the solution.
Graph the two functions and find point of intersection. Follow the screens across from left to right in row one and in row two.
Section 3.4 Solving Rational Equations & Radical Equations 282/6. Solve
See instructions for this method at http://cfcc.edu/faculty/cmoore/ti­intersect.htm
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171S3.4 Solving Rational Equations and Radical Equations
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Section 3.4 Solving Rational Equations & Radical Equations 282/18. Solve
Section 3.4 Solving Rational Equations & Radical Equations 282/22. Solve
Section 3.4 Solving Rational Equations & Radical Equations Section 3.4 Solving Rational Equations & Radical Equations 282/32. Solve
282/36. Solve
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171S3.4 Solving Rational Equations and Radical Equations
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Section 3.4 Solving Rational Equations & Radical Equations Section 3.4 Solving Rational Equations & Radical Equations 283/58. Solve
283/76. Solve
Section 3.4 Solving Rational Equations & Radical Equations Section 3.4 Solving Rational Equations & Radical Equations 283/82. Solve
283/78. Solve m1/2 = ­7
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171S3.4 Solving Rational Equations and Radical Equations
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Section 3.4 Solving Rational Equations & Radical Equations Section 3.4 Solving Rational Equations & Radical Equations 283/84. Solve
282/14. Solve
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