What are some examples of extraneous solutions to equations?
1 Answer
Example 1 : Raising to an even power
Solve
Raising both sides to the
This requires,
Factoring gives
So we need
The solution set of the last equation is
Example 2 Multiplying by zero
If you solve
you'll get
which lead to
.
It looks like the solution set is
Both are solutions to the second and third equations, but
Example 3 : Combining sums of logarithms.
Solve:
Combine the logs on the left to get
This leads to