FreeAlgebra Tutorials!

Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

# Conjugates

Now we will work with special pairs of binomial radical expression such as the following:

Notice that in each binomial pair, the first terms are the same and the second terms differ only in sign.

Such pairs of binomial radical expressions are called conjugates.

Definition â€” Conjugates

Two binomial radical expressions of the form are called conjugates.

Here, a, b, c, and d are rational numbers. Also, and are not both rational.

The product of conjugates is a rational number.

Example 1

Find:

 Solution Use the FOIL method. Multiply. The two middle terms are opposites and add to zero. = 10 - 9Â· 2 Simplify. = 10 - 18 = -8 Thus,