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Expert: - 5/29/2009


Question
Hello, I have a question which I havent been able to answer.

My teacher gave me my final last week and I encountered a question that stumped me. I couldnt even answer it and I still cant.
It goest like this:

2^x + 2^-x= 3
Solve for x

I couldnt figure out how to solve it and I've tried everything I know. Its been driving me crazy. Any help would be apreciated. Thanks.

Answer
Use Excel.

Put 0 in A1, 2 in A2.
Put =A1-B1*(A2-A1)/(B2-B1) in A3.

Put =2^A1+2^-A1-3 in B1.  Copy B1 to B2.  Copy B2 to B3.

Goto A3, press F8, and move one cell to the right.
Press Control-C (Cntl and 'C' at the same time).
Down arrow to A4.  Press Control-V.
Down again, control-V again,
repeat last line a half dozen times.

Here is what I got in column A:
0
2
0.888888889
1.252570545
1.427640769
1.385937381
1.388437955
1.388483882
1.388483827
1.388483827

and here is column B:
-1
1.25
-0.608220706
-0.19764448
0.061802806
-0.003942128
-7.10968E-05
8.42472E-08
-1.79723E-12
0.

Since column B is the functional value at whatever is in A,
it can be seen that the function is 0 when column A has
1.388483827 as the value.

I would recommend doing this on you're computer just for the exercise of it and learning how to use Excel (if you don't already know it, that is).  

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