Printable View

- December 15th 2007, 03:40 PMHasan1Solving
- December 15th 2007, 05:08 PMSoltras
Arrange it all on one side so it's

.

Now the strategy is to factor the left side to get smaller pieces that are forced to be equal to zero.

Start by recalling and , so multiply through by .

You get:

.

Now remember . So:

.

And now we can make our first factor, which is .

.

No we know when (in your range), so that is one solution. Let's forget about that factor now and concentrate on the rest:

.

Recall that , and apply this to the middle term:

Simplifies to:

.

Now, remember that , so we now have:

.

But refer again to the fact that . so we have:

.

Apply the above identity again:

.

Now solve for by just isolating it the old fashioned way. From this, you should get two more values in the interval to , making three values total because of the one we found earlier.