Download Lesson 96: Difference of Two Squares Theorem

Bell Work:
What are the four types of
non-linear functions
discussed in yesterday’s
lesson?
Answer:
Quadratic, Cubic, Square
Root and Absolute Value
Lesson 96:
Difference of
Two Squares
Theorem
In Lesson 62 we introduced the
topic of square roots and
noted that every positive real
number has both a positive
square root and a negative
square root. Because 2 times 2
equals 4 and -2 times -2 also
equals 4, we say that the two
square roots of 4 are +2 and -2.
When we use the radical
sign, √ , to indicate the
square root of a positive
number, we are
designating the principal
or positive square root.
For example,
√4 = 2
If we wish to indicate the
negative square root, we
must use a minus sign in
front of the radical. For
example, to designate the
negative square root of 4,
we must write
-√4 which equals -2
If we are asked to find the
numbers that satisfy the
equation
2
x=4
We know that the numbers
are +2 and -2 because
2
2
(+2) = 4 and also (-2) = 4
The general form of the
2
2
2
equation x = 4 is p = q .
The theorem that describes
the solution to an equation
of the form p2= q 2 is called
the difference of two
squares theorem.
Difference of two squares
theorem: if p and q are
2
2
real numbers and if p = q,
then p = q or p = -q.
A quadratic equation in x has an
x 2 term as the highest power of
the variable. A quadratic
2
equation in p has a p term as the
highest power of the variable. It is
very important to realize that in
the beginning of the book the ±
sign arises only in the solution of a
quadratic equation. For example,
2
if m = 3 then m = ±√3
Example:
2
Solve p = 16
Answer:
p = ±4
Example:
2
Solve p = 41
Answer:
p = ±√41
Example:
2
Solve k = 13
Answer:
k = ±√13
HW: Lesson 96 #1-30