Exponential Functions
Solving Radical Equations
Solving Radical Equations
To solve a radical equation, perform inverse operations in the usual way. But
take note:
= | a|
, and thus expressions such as
must be solved as absolute value expressions for more on solving
equations containing absolute values. It is not necessary to solve
(
)2
as an absolute value expression.
Example: Solve for
x
:
(x + 5)2 = 18
.
=
.
| x + 5| = 3.
x + 5 = 3
x = 3
Since we cannot take the square root of a negative number, there
are often numbers which appear to be solutions but do not actually make the
equation true. For example, we get two solutions when we solve
= - 2x
:
()2 = (- 2x)2
.
6x + 10 = 4x
2
.
4x
2 - 6x - 10 = 0
.
2(2x
2 - 3x - 5) = 0
.
2(x + 1)(2x - 5) = 0
.
x = - 1
or
.
We can plug -1 in for
x
in the original equation to check that it makes the
equation true:
= - 2(- 1)
?
= 2
? Yes.
True.
However, when we plug
in for
x
:
= - 2()
?
= - 5
? No.
False.
is an extraneous solution, and the only solution to
= - 2x
is
x = - 1
.
As demonstrated by this example, we must check all "solutions" and eliminate false solutions.
