7 – 67 – 6Solving Rational EquationsSolving Rational Equations

Day 2Day 2

Objective: Solve equations that contain radicals or rational exponents.

Example 4

Solve 3 2 2 0x x

Solution

2 2

3 2 2 0

3 2 2

3 2 2

3 2 4

2

x x

x x

x x

x x

x

Check solution:

3 2 2 2 2 0

6 2 2 2 0

8 2 2 0

4 2 2 2 0

2 2 2 2 0

Raising both sides of an equation to the same power may introduce extraneous solutions.

What does extraneous mean?

Main Entry: ex·tra·ne·ous Pronunciation: ek-'strA-nE-&sFunction: adjectiveEtymology: Latin extraneus -- more at STRANGE1 : existing on or coming from the outside2 a : not forming an essential or vital part <extraneous ornamentation> b : having no relevance <an extraneous digression>3 : being a number obtained in solving an equation that is not a solution of the equation <extraneous roots>

When you use this procedure it is essential that you check each solution. In the original equation.

Example 5

Solve

22

2

2

4 2

4 2

8 16 2

10 16 0

2 8 0

2 0 or 8 0

2 8

x x

x x

x x x

x x

x x

x x

x x

4 2x x

Solution

Check the solutions

4 2

2 4 2 2

2 4

2 2

x x

4 2

8 4 2 8

4 16

x x

The only solution that works is 8.

Home work page 441, 47 – 54 all.