Conjugates
Recall the special product rule (a + b)(a - b) = a2 - b2. The product of the sum
 and the difference
 can be found by using this rule:
The product of the irrational number
and the irrational number
is
the rational number 13. For this reason the expressions
and
are called conjugates
of one another.
Helpful hint
The word “conjugate†is used
in many contexts in mathematics.
According to the
dictionary, conjugate means
joined together, especially as
in a pair.
Example 1
Multiplying conjugates
Find the products. Assume the variables represent positive real numbers.
Solution
|