Transcript Chapter 9, Section 6

Solving Equations with Radicals
Copyright © 2010 Pearson Education, Inc. All rights reserved
Sec 9.6 - 1
Solving Equations with Radicals
EXAMPLE 1
Solve
Using the Power Rule
5x – 6 = 7.
Solving Equations with Radicals
EXAMPLE 1
Solve
Using the Power Rule
5x – 6 = 7.
5x – 6
5 · 11 – 6
= 7
= 7 ? Let x = 11.
7 = 7 True
Since 11 satisfies the original equation, the solution set is { 11 }.
Copyright © 2010 Pearson Education, Inc. All rights reserved.
Solving Equations with Radicals
Solving an Equation with Radicals
Solving an Equation with Radicals
Step 1
Isolate the radical. Make sure that one radical term is alone on
one side of the equation.
Step 2
Apply the power rule. Raise both sides of the equation to a
power that is the same as the index of the radical.
Step 3
Solve. Solve the resulting equation; if it still contains a radical,
repeat Steps 1 and 2.
Step 4
Check all potential solutions in the original equation.
Copyright © 2010 Pearson Education, Inc. All rights reserved.
Solving Equations with Radicals
EXAMPLE 2
Solve
Using the Power Rule
2x – 9 + 1 = 0.
Solving Equations with Radicals
EXAMPLE 3
Solve
Using the Power Rule; Squaring a Binomial
9 – x = x + 3.
Solving Equations with Radicals
EXAMPLE 4
Solve
Using the Power Rule; Squaring a Binomial
x2 – 8x + 3 = x – 5.
Solving Equations with Radicals
EXAMPLE 5
Solve
x + 7 +
Using the Power Rule; Squaring Twice
–x + 6 = 5.