Solve the equation for
You begin by transforming the equation to get the -term on its own:
This has the solutions
First, you continue with (1):
Then you continue with (2):
The problem tells you to find all the solutions that are in the interval . You find these by considering and with respect to that interval.
Look at first. If you insert , you get
which is in the interval. When you check , you get
Then you check ,
which is also in the interval. Now you notice that if you check , the answer will be outside the interval . That means you have found all the solutions for .
Now you have to do the same for . The values still have to be in the interval for them to be a part of the solution. That gives you
As you can see, the last value is outside the interval. That means the solutions in the interval are: