Intermediate Algebra (11th edition)

Multiply by the

conjugate.

i 2 =- 1

1 a+b 21 a-b 2 =a^2 - b^2

8.6 Solving Equations with Radicals

Solving an Equation with Radicals

Step 1 Isolate one radical on one side of the equation.

Step 2 Raise both sides of the equation to a power that
is the same as the index of the radical.

Step 3 Solve the resulting equation. If it still contains
a radical, repeat Steps 1 and 2.

Step 4 Check all proposed solutions in the original
equation.

Solve

Subtractx.

Square each side.

Apply the exponents.

Standard form

Factor.

or Zero-factor property

or Solve each equation.

A check shows that 3 is a solution, but is extraneous. The solution

set is 536.

- 1

x= 3 x=- 1

x- 3 = 0 x+ 1 = 0

1 x- 321 x+ 12 = 0

x^2 - 2 x- 3 = 0

2 x+ 3 =x^2

(^) A 22 x+ (^3) B^2 =x^2
22 x+ 3 =x
22 x+ 3 - x=0.

CONCEPTS EXAMPLES

486 CHAPTER 8 Roots, Radicals, and Root Functions

8.7 Complex Numbers

where

For any positive number b,

To multiply radicals with negative radicands, first
change each factor to the form and then multiply.
The same procedure applies to quotients.

Adding and Subtracting Complex Numbers
Add (or subtract) the real parts and add (or subtract) the
imaginary parts.

Multiplying Complex Numbers
Multiply complex numbers by using the FOIL method.

Dividing Complex Numbers
Divide complex numbers by multiplying the numera-
tor and the denominator by the conjugate of the
denominator.

i 2 b

2 bi 2 b.

i 2  1 , i^2 1.

FOIL

Multiply.

Combine real terms.

= 213 - i 2 , or 6 - 2 i

=

2013 - i 2

10

=

2013 - i 2

9 - i^2

=

2013 - i 2

13 +i 213 - i 2

20

3 +i

= 13 - i

= 10 - i+ 3

= 10 - i- 31 - 12 i^2 =- 1

= 10 - 6 i+ 5 i- 3 i^2

12 +i 215 - 3 i 2

= 13 - 4 i =- 3 + 10 i

15 + 3 i 2 + 18 - 7 i 2 15 + 3 i 2 - 18 - 7 i 2

2 - 18

2 - 2

=

i 218

i 22

=

B

18

2

= 29 = 3

=- 9

=- 1 # 9 i^2 =- 1

=i^2281

=i 23 #i 227 2 - b=i 2 b

2 - 3 # 2 - 27

2 - 25 =i 225 = 5 i